wish to creat a class called Matrix as a base

#include<iostream.h>
#include<conio.h>


class Matrix
{
public:    // constructors
    Matrix()
    {    //printf("Executing constructor Matrix() ...\n");
        // create a Matrix object without content
        p = NULL;
        rows = 0;
        cols = 0;
    }
    Matrix(const int row_count, const int column_count)
    {    // create a Matrix object with given number of rows and columns
        //printf("Executing constructor Matrix(const int column_count, const int row_count) ...\n");
        p = NULL;
        if (row_count > 0 && column_count > 0)
        {
            rows = row_count;
            cols = column_count;
            p = new double*[rows];
            for (int r = 0; r < rows; r++)
            {
                p[r] = new double[rows];
                // initially fill in zeros for all values in the matrix;
                for (int c = 0; c < cols; c++)
                {
                    p[r][c] = 0;
                }
            }
        }
    }
    // assignment operator
    Matrix(const Matrix& a)
    {
        //printf("Executing constructor Matrix(const Matrix& a) ...\n");
        rows = a.rows;
        cols = a.cols;
        p = new double*[a.rows];
        for (int r = 0; r < a.rows; r++)
        {
            p[r] = new double[a.cols];
            // copy the values from the matrix a
            for (int c = 0; c < a.cols; c++)
            {
                p[r][c] = a.p[r][c];
            }
        }
    }
    // index operator. You can use this class like myMatrix(col, row)
    // the indexes are one-based, not zero based.
 double& operator()(const int r, const int c)
 {
        //printf("Executing Matrix operator() ...\n");
       if (p != NULL && r > 0 && r <= rows && c > 0 && c <= cols)
       {
           return p[r-1][c-1];
        }
       else
       {
            throw Exception("Subscript out of range");
        }
    }
    // assignment operator
    Matrix& operator= (const Matrix& a)
    {
        //printf("Executing Matrix operator= ...\n");
        rows = a.rows;
        cols = a.cols;
        p = new double*[a.rows];
        for (int r = 0; r < a.rows; r++)
        {
            p[r] = new double[a.cols];
            // copy the values from the matrix a
            for (int c = 0; c < a.cols; c++)
            {
                p[r][c] = a.p[r][c];
            }
        }
        return *this;
    }
    // operator addition 1
    friend Matrix operator+(const Matrix& a, const Matrix& B)
    {
        // check if the dimensions match
       /* if (a.rows == b.rows && a.cols == b.cols)*/
        {
          Matrix res(a.rows, a.cols);
            for (int r = 0; r < a.rows; r++)
            {
                for (int c = 0; c < a.cols; c++)
                {
                 //   res.p[r][c] = a.p[r][c] + b.p[r][c];
                }
            }
          return res;
        }
 else
        {
            // give an error
            throw Exception("Dimensions does not match");
        }
        // return an empty matrix (this never happens but just for safety)
        return Matrix();
    }
    // add a double value (elements wise)
    Matrix& add(double v)
    {
        for (int r = 0; r < rows; r++)
        {
            for (int c = 0; c < cols; c++)
            {
                p[r][c] += v;
            }
        }
      return *this;
    }
    // subtract a double value (elements wise)
    Matrix& subtract(double v)
    {
        return add(-v);
    }
    // multiply a double value (elements wise)
    Matrix& multiply(double v)
    {
        for (int r = 0; r < rows; r++)
        {
            for (int c = 0; c < cols; c++)
            {
                p[r][c] *= v;
            }
        }
      return *this;
    }
    // operator subtraction 2
    friend Matrix operator- (const Matrix& a, const Matrix& b)
    {
        // check if the dimensions match
        if (a.rows == b.rows && a.cols == b.cols)
        {
          Matrix res(a.rows, a.cols);
            for (int r = 0; r < a.rows; r++)
            {
                for (int c = 0; c < a.cols; c++)
                {
                    res.p[r][c] = a.p[r][c] - b.p[r][c];
                }
            }
          return res;
        }
        else
        {
            // give an error
            throw Exception("Dimensions does not match");
        }
        // return an empty matrix (this never happens but just for safety)
        return Matrix();
    }
    // operator unary minus
    friend Matrix operator- (const Matrix& a)
    {
      Matrix res(a.rows, a.cols);
        for (int r = 0; r < a.rows; r++)
        {
            for (int c = 0; c < a.cols; c++)
            {
                res.p[r][c] = -a.p[r][c];
            }
        }
   
        return res;
    }
   
    // operator multiplication 3
    friend Matrix operator* (const Matrix& a, const Matrix& B)
    {
        // check if the dimensions match
        if (a.cols == b.rows)
        {
          Matrix res(a.rows, b.cols);
            for (int r = 0; r < a.rows; r++)
            {
                for (int c_res = 0; c_res < b.cols; c_res++)
                {
                    for (int c = 0; c < a.cols; c++)
                    {
                        res.p[r][c_res] += a.p[r][c] * b.p[c][c_res];
                    }
                }
            }
          return res;
        }
        else
        {
            // give an error
            throw Exception("Dimensions does not match");
        }
        // return an empty matrix (this never happens but just for safety)
        return Matrix();
    }
    /*
     * returns the minor from the given matrix where
     * the selected row and column are removed
     */
    Matrix minor(const int row, const int col)
    {
        //printf("minor(row=%i, col=%i), rows=%i, cols=%i\n", row, col, rows, cols);
        Matrix res;
       if (row > 0 && row <= rows && col > 0 && col <= cols)
       {
            res = Matrix(rows - 1, cols - 1);
           
            // copy the content of the matrix to the minor, except the selected
            for (int r = 1; r <= (rows - (row >= rows)); r++)
            {
                for (int c = 1; c <= (cols - (col >= cols)); c++)
                {
                    //printf("r=%i, c=%i, value=%f, rr=%i, cc=%i \n", r, c, p[r-1][c-1], r - (r > row), c - (c > col));
                    res(r - (r > row), c - (c > col)) = p[r-1][c-1];
                }
            }       
        }
        else
        {
            throw Exception("Index for minor out of range");
        }
       
        return res;
    }
   
    /*
     * returns the size of the i-th dimension of the matrix.
     * i.e. for i=1 the function returns the number of rows,
     * and for i=2 the function returns the number of columns
     * else the function returns 0
     */
    int size(const int i)
    {
        if (i == 1)
        {
            return rows;
        }
        else if (i == 2)
        {
            return cols;
        }
        return 0;
    }
    // returns the number of rows
    int get_rows()
    {
        return rows;
    }
   
    // returns the number of columns
    int get_cols()
    {
        return cols;
    }
    // print the contents of the matrix
    void print()
    {
        if (p != NULL)
        {
            printf("[");
            for (int r = 0; r < rows; r++)
            {
                if (r > 0)
                {
                    printf(" ");
                }
                for (int c = 0; c < cols-1; c++)
                {
                    printf("%.2f, ", p[r][c]);
                }
                if (r < rows-1)
                {
                    printf("%.2f;\n", p[r][cols-1]);
                }
                else
                {
                    printf("%.2f]\n", p[r][cols-1]);
                }
            }
        }
        else
        {
            // matrix is empty
            printf("[ ]\n");
        }
    }
public:
    // destructor
    ~Matrix()
    {
        // clean up allocated memory
        for (int r = 0; r < rows; r++)
        {
            delete p[r];
        }
        delete p;
        p = NULL;
    }
private:
    int rows;
    int cols;
    double** p;         // pointer to a matrix with doubles
};
/*
 * i.e. for i=1 the function returns the number of rows,
 * and for i=2 the function returns the number of columns
 * else the function returns 0
 */
int size(Matrix& a, const int i)
{
    return a.size(i);
}

// addition of Matrix with double
Matrix operator+ (const Matrix& a, const double B)
{
    Matrix res = a;
    res.add(B);
    return res;
}
// addition of double with Matrix
Matrix operator+ (const double b, const Matrix& a)
{
    Matrix res = a;
    res.add(b);
    return res;
}
// subtraction of Matrix with double
Matrix operator- (const Matrix& a, const double B)
{
    Matrix res = a;
    res.subtract(B);
    return res;
}
// subtraction of double with Matrix
Matrix operator- (const double b, const Matrix& a)
{
    Matrix res = -a;
    res.add(b);
    return res;
}
// multiplication of Matrix with double
Matrix operator* (const Matrix& a, const double B)
{
    Matrix res = a;
    res.multiply(B);
    return res;
}
// multiplication of double with Matrix
Matrix operator* (const double b, const Matrix& a)
{
    Matrix res = a;
    res.multiply(b);
    return res;
}

/**
 * returns a matrix with size cols x rows with ones as values
 */
Matrix ones(const int rows, const int cols)
{
    Matrix res = Matrix(rows, cols);
    for (int r = 1; r < rows; r++)
    {
        for (int c = 1; c <= cols; c++)
        {
            res(r, c) = 1;
        }
    }
    return res;
}
/**
 * returns a matrix with size cols x rows with zeros as values
 */
Matrix zeros(const int rows, const int cols)
{
    return Matrix(rows, cols);
}

/**
 * returns a diagonal matrix with size n x n with ones at the diagonal
 * @param   v a vector
 * @return  a diagonal matrix with ones on the diagonal
 */
Matrix diag(const int n)
{
    Matrix res = Matrix(n, n);
    for (int i = 1; i <= n; i++)
    {
        res(i, i) = 1;
    }
    return res;
}
/**
 * returns a diagonal matrix
 * @param   v a vector
 * @return  a diagonal matrix with the given vector v on the diagonal
 */
Matrix diag(Matrix& v)
{
    Matrix res;
    if (v.get_cols() == 1)
    {
        // the given matrix is a vector n x 1
        int rows = v.get_rows();
        res = Matrix(rows, rows);
       
        // copy the values of the vector to the matrix
        for (int r=1; r <= rows; r++)
        {
            res(r, r) = v(r, 1);
        }
    }
    else if (v.get_rows() == 1)
    {
        // the given matrix is a vector 1 x n
        int cols = v.get_cols();
        res = Matrix(cols, cols);
        // copy the values of the vector to the matrix
        for (int c=1; c <= cols; c++)
        {
            res(c, c) = v(1, c);
        }       
    }
    else
    {
        throw Exception("Parameter for diag must be a vector");
    }
    return res;
}
/*
 * returns the determinant of Matrix a
 */
double det(Matrix& a)
{
    double d = 0;       // value of the determinant
    int rows = a.get_rows();
    int cols = a.get_cols();
   
    if (rows == cols)
    {
        // this is a square matrix
        if (rows == 1)
        {
            // this is a 1 x 1 matrix
            d = a(1, 1);
        }
        else if (rows == 2)
        {
            // this is a 2 x 2 matrix
            // the determinant of [a11,a12;a21,a22] is det = a11*a22-a21*a12
            d = a(1, 1) * a(2, 2) - a(2, 1) * a(1, 2);
        }
        else
        {
            // this is a matrix of 3 x 3 or larger
            for (int c = 1; c <= cols; c++)
            {
                Matrix M = a.minor(1, c);
                //d += pow(-1, 1+c)  * a(1, c) * det(M);
                d += (c%2 + c%2 - 1) * a(1, c) * det(M);  // faster than with pow()
            }
        }
    }
    else
    {
        throw Exception("Matrix must be square");
    }
    return d;
}
// swap two values
void swap(double& a, double& b)
{
    double temp = a;
    a = b;
    b = temp;
}
/*
 * returns the inverse of Matrix a
 */
Matrix inv(Matrix& a)
{
    Matrix res;
    double d = 0;       // value of the determinant
    int rows = a.get_rows();
    int cols = a.get_cols();
   
    d = det(a);
    if (rows == cols && d != 0)
    {
        // this is a square matrix
        if (rows == 1)
        {
            // this is a 1 x 1 matrix
            res = Matrix(rows, cols);
            res(1, 1) = 1 / a(1, 1);
        }
        else if (rows == 2)
        {
            // this is a 2 x 2 matrix
            res = Matrix(rows, cols);
            res(1, 1) = a(2, 2);
            res(1, 2) = -a(1, 2);
            res(2, 1) = -a(2, 1);
            res(2, 2) = a(1, 1);
            res = (1/d) * res;
        }
        else
        {
            // this is a matrix of 3 x 3 or larger
            // calculate inverse using gauss-jordan elimination
            //      [url="http://mathworld.wolfram.com/MatrixInverse.html"]http://mathworld.wolfram.com/MatrixInverse.html[/url]
            //      [url="http://math.uww.edu/~mcfarlat/inverse.htm"]http://math.uww.edu/~mcfarlat/inverse.htm[/url]
            res = diag(rows);     // a diagonal matrix with ones at the diagonal
            Matrix ai = a;        // make a copy of Matrix a
            for (int c = 1; c <= cols; c++)
            {
                // element (c, c) should be non zero. if not, swap content
                // of lower rows
                int r;
                for (r = c; r <= rows && ai(r, c) == 0; r++)
                {
                }               
                if (r != c)
                {
                    // swap rows
                    for (int s = 1; s <= cols; s++)
                    {
                        swap(ai(c, s), ai(r, s));
                        swap(res(c, s), res(r, s));
                    }
                }
                // eliminate non-zero values on the other rows at column c
                for (int r = 1; r <= rows; r++)
                {
                    if(r != c)
                    {
                        // eleminate value at column c and row r
                        if (ai(r, c) != 0)
                        {
                            double f = - ai(r, c) / ai(c, c);
                           
                            // add (f * row c) to row r to eleminate the value
                            // at column c
                            for (int s = 1; s <= cols; s++)
                            {
                                ai(r, s) += f * ai(c, s);
                                res(r, s) += f * res(c, s);
                            }
                        }                   
                    }
                    else
                    {
                        // make value at (c, c) one,
                        // divide each value on row r with the value at ai(c,c)
                        double f = ai(c, c);
                        for (int s = 1; s <= cols; s++)
                        {
                            ai(r, s) /= f;
                            res(r, s) /= f;
                        }                       
                    }
                }               
            }
        }
    }
    else
    {
        if (rows == cols)
        {
            throw Exception("Matrix must be square");
        }
        else
        {
            throw Exception("Determinant of matrix is zero");
        }
    }
    return res;
}

int main(int argc, char *argv[])
{
    try
    {
        // create an empty matrix of 3x3 (will initially contain zeros)
        int cols = 3;
        int rows = 3;
        Matrix A = Matrix(cols, rows);
        // fill in some values in matrix a
        int count = 0;
        for (int r = 1; r <= rows; r++)
        {
            for (int c = 1; c <= cols; c++)
            {
                count ++;
                A(r, c) = count;
            }
        }
        // adjust a value in the matrix  (indexes are one-based)
        A(2,1) = 1.23;
        // read a value from the matrix  (indexes are one-based)
        double centervalue = A(2,2);
        printf("centervalue = %f \n", centervalue);
        printf("\n");
        // print the whole matrix
        printf("A = \n");
        A.print();
        printf("\n");
        Matrix B = ones(rows, cols) + diag(rows);
        printf("B = \n");
        B.print();
        printf("\n");
        Matrix B2 = Matrix(rows, 1);        // a vector
        count = 1;
        for (int r = 1; r <= rows; r++)
        {
            count ++;
            B2(r, 1) = count * 2;
        }
        printf("B2 = \n");
        B2.print();
        printf("\n");
       
        Matrix C;
        C = A + B;
        printf("A + B = \n");
        C.print();
        printf("\n");
        C = A - B;
        printf("A - B = \n");
        C.print();
        printf("\n");
        C = A * B2;
        printf("A * B2 = \n");
        C.print();
        printf("\n");
        // create a diagonal matrix
        Matrix E = diag(B2);
        printf("E = \n");
        E.print();
        printf("\n");
        // calculate determinant
        Matrix D = Matrix(2, 2);
        D(1,1) = 2;
        D(1,2) = 4;
        D(2,1) = 1;
        D(2,2) = -2;
        printf("D = \n");
        D.print();
        printf("det(D) = %f\n\n", det(D));
        printf("A = \n");
        A.print();
        printf("\n");
        printf("det(A) = %f\n\n", det(A));
       
        Matrix F;
        F = 3 - A ;
        printf("3 - A = \n");
        F.print();
        printf("\n");
       
        // test inverse
        Matrix G = Matrix(2, 2);
        G(1, 1) = 1;
        G(1, 2) = 2;
        G(2, 1) = 3;
        G(2, 2) = 4;
        printf("G = \n");
        G.print();
        printf("\n");
        Matrix G_inv = inv(G);
        printf("inv(G) = \n");
        G_inv.print();
        printf("\n");
       
        Matrix A_inv = inv(A);
        printf("inv(A) = \n");
        A_inv.print();
        printf("\n");
    }
    catch (Exception err)
    {
        printf("Error: %s\n", "err.msg");
    }
    catch (...)
    {
        printf("An error occured...\n");
    }
    printf("\n");
    system("PAUSE");
    return EXIT_SUCCESS;
}