Program for matrix operations like determinant, singular, etc.

Program for matrix operations like determinant, singular, etc.(Source Code)
#include
#include
#include
using namespace std;


const int MAX = 3 ;

class matrix
{
    private :

        int mat[MAX][MAX] ;

    public :

        matrix( ) ;
        void create( ) ;
        void display( ) ;
        matrix matmul ( matrix &m ) ;
        matrix transpose( ) ;
               int determinant( ) ;
        int isortho( ) ;
} ;

// initializes the matrix mat with 0
matrix :: matrix( )
{
    for ( int i = 0 ; i < MAX ; i++ )
    {
        for ( int j = 0 ; j < MAX ; j++ )
            mat[i][j] = 0 ;
    }
}

// creates matrix mat
void matrix :: create( )
{
    int n ;
    for ( int i = 0 ; i < MAX ; i++ )
    {
        for ( int j = 0 ; j < MAX ; j++ )
        {
            cout << "\nEnter the element: " ;
            cin >> n ;
            mat[i][j] = n ;
        }
    }
}

// displays the contents of matrix
void matrix :: display( )
{
    for ( int i = 0 ; i < MAX ; i++ )
    {
        for ( int j = 0 ; j < MAX ; j++ )
            cout << mat[i][j] << "  " ;
        cout << endl ;
    }
}

// multiplies two matrices
matrix matrix :: matmul ( matrix &m )
{
    matrix m1 ;
    for ( int k = 0 ; k < MAX ; k++ )
    {
        for ( int i = 0 ; i < MAX ; i++ )
        {
            for ( int j = 0 ; j < MAX ; j++ )
                m1.mat[k][i] += mat[k][j] * m.mat[j][i] ;
        }
    }
    return m1 ;
}

// obtains transpose of matrix m1
matrix matrix :: transpose( )
{
    matrix m ;
    for ( int i = 0 ; i < MAX ; i++ )
    {
        for ( int j = 0 ; j < MAX ; j++ )
             m.mat[i][j] = mat[j][i] ;
    }
    return m ;
}

// finds the determinant value for given matrix
int matrix :: determinant( )
{
    int sum, j, k, p ;
    sum = 0 ; j = 1 ; k = MAX - 1 ;

    for ( int i = 0 ; i < MAX ; i++ )
    {
            p = pow ( -1, i ) ;

                if ( i == MAX - 1 )
                    k = 1 ;
        sum = sum + ( mat[0][i] * ( mat[1][j] *
                    mat[2][k] - mat[2][j] *
                    mat[1][k] ) ) * p ;
        j = 0 ;
     }

    return sum ;
}

// checks if given matrix is an orthogonal matrix
int matrix :: isortho( )
{
    int i;
    // transpose the matrix ;
    matrix m1 = transpose( ) ;

    // multiply the matrix with its transpose
    matrix m2 = matmul ( m1 ) ;

    // check for the identity matrix
    for (  i = 0  ; i < MAX ; i++ )
    {
        if ( m2.mat[i][i] == 1 )
            continue ;
        else
            break ;
    }
    if ( i == MAX )
        return 1 ;
    else
        return 0 ;
}

int main( )
{
    matrix mat1 ;
    cout << "\nEnter elements for first array: \n" ;
    mat1.create( ) ;

     cout << "\nThe Matrix: " << endl ;
    mat1.display( ) ;

    int d = mat1.determinant( ) ;
       cout << "\nThe determinant for given matrix: " << d << endl ;

    if ( d == 0  )
            cout << "\nmat1 matrix is singular" << endl ;
    else
            cout << "\nmat1 matrix  is not singular" << endl ;

    d = mat1.isortho( ) ;
    if ( d != 0 )
        cout << "\nmat1 matrix is orthogonal" << endl ;
    else
        cout << "\nmat1 matrix is not orthogonal" << endl ;
        getch();
}