A matrix header file that allows for matrix addition, subtraction, and multiplication with method calls & operator overloading

Matrix.h

#ifndef _MATRIX
#define _MATRIX

/*
Matrix Header File

Matrix library that allows creation, addition,
subtraction, and multiplication of matrices.
2 Dimensional matrices only

Alex Marroquin
DATE: 7/14/2015
*/

#include<vector>
#include<iostream>

using namespace std;

class Matrix {
public:
	int rows, col;
	vector< vector<double> > mat;
	Matrix();
	Matrix(int, int);
	void print();
	Matrix add(Matrix, Matrix);
	Matrix sub(Matrix, Matrix);
	Matrix multiply(Matrix, Matrix);
	Matrix& operator+(const Matrix&);
	Matrix& operator=(const Matrix&);
	Matrix& operator-(const Matrix&);
	Matrix& operator*(const Matrix&);
};

// Initialize with a default 2 X 2 matrix
Matrix::Matrix()
{
	rows = 2;
	col = 2;

	for (int i = 0; i < rows; i++)
	{
		vector<double> rw;
		for (int j = 0; j < col; j++)
			rw.push_back(0);
		mat.push_back(rw);
	}
}

// Create an r X c matrix
Matrix::Matrix(int r, int c)
{
	rows = r;
	col = c;

	for (int i = 0; i < rows; i++)
	{
		vector<double> rw;
		for (int j = 0; j < col; j++)
			rw.push_back(0);
		mat.push_back(rw);
	}
}

// Display the matrix on screen
void Matrix::print()
{
	for (int i = 0; i < rows; i++)
	{
		for (int j = 0; j < col; j++)
			cout << mat[i][j] << " ";
		cout << endl;
	}
}

// Add 2 matrices w/o operator overloading
Matrix Matrix::add(Matrix A, Matrix B)
{
	if (A.rows != B.rows || A.col != B.col) // sizes do not match
	{
		Matrix Z(0, 0);
		return Z;
	}

	Matrix C(A.rows, A.col); // Creates new matrix to store values

	for (int i = 0; i < C.rows; i++)
	{
		for (int j = 0; j < C.col; j++)
			C.mat[i][j] = A.mat[i][j] + B.mat[i][j];
	}

	return C;
}

// Subtract 2 matrices
Matrix Matrix::sub(Matrix A, Matrix B)
{
	if (A.rows != B.rows || A.col != B.col)
	{
		Matrix Z(0, 0);
		return Z;
	}

	Matrix C(A.rows, A.col);

	for (int i = 0; i < C.rows; i++)
	{
		for (int j = 0; j < C.col; j++)
			C.mat[i][j] = A.mat[i][j] - B.mat[i][j];
	}
	return C;
}

Matrix Matrix::multiply(Matrix A, Matrix B)
{
	Matrix C(A.rows, B.col);
	if (A.col != B.rows)
		return C;

	for (int i = 0; i < C.rows; i++)
	{
		for (int j = 0; j < C.col; j++)
		{
			for (int k = 0; k < A.col; k++)
				C.mat[i][j] += A.mat[i][k] * B.mat[k][j];
		}
	}
	return C;
}

//Overloaded operators based one the ones above

Matrix& Matrix::operator=(const Matrix&M)
{
	mat.clear();
	rows = M.rows;
	col = M.col;

	for (int i = 0; i < rows; i++)
	{
		vector<double> rw;
		for (int j = 0; j < col; j++)
			rw.push_back(M.mat[i][j]);
		mat.push_back(rw);
	}
	
	return *this;
}

Matrix& Matrix::operator+(const Matrix &M)
{

	if (M.rows != rows || M.col != col)
		return *this;

	Matrix *C = new Matrix(M.rows, M.col);

	for (int i = 0; i < M.rows; i++)
	{
		for (int j = 0; j < M.col; j++)
			C->mat[i][j] = this->mat[i][j] + M.mat[i][j];
	}
	return *C;
}

Matrix& Matrix::operator-(const Matrix &M)
{
	// *this is the 1st operand while M is the 2nd operand
	if (M.rows != rows || M.col != col)
		return *this;

	Matrix *C = new Matrix(M.rows, M.col);

	for (int i = 0; i < M.rows; i++)
	{
		for (int j = 0; j < M.col; j++)
			C->mat[i][j] = this->mat[i][j] - M.mat[i][j];
	}
	return *C;
}

Matrix& Matrix::operator*(const Matrix &M)
{
	// *this is the 1st operand while M is the 2nd operand
	Matrix *C = new Matrix(rows, M.col);
	if (col != M.rows)	//Check that the columns and rows match
		return *C;

	for (int i = 0; i < C->rows; i++)
	{
		for (int j = 0; j < C->col; j++)
		{
			for (int k = 0; k < M.col; k++)
				C->mat[i][j] += mat[i][k] * M.mat[k][j];
		}
	}
	return *C;
}

#endif