What should the matrix class method return?

Question

C++ / C#

I am writing a square matrix class, here, in fact, the class itself:

matrix.h

#ifndef MATRIX_H
#define MATRIX_H

#include <string.h>

class Matrix
{
private:
    std::string name;
    double      **matrix;
    int         size;
public:
    // Default constructor
    Matrix() : name("NaN"), matrix(nullptr), size(0)
    { }

    // Constructor with values
    Matrix(std::string nm, int sz) : name(nm), size(sz)
    {
        try 
        {
            matrix = new double *[size];
            for(int i = 0; i < size; i++)
                matrix[i] = new double[size];
        }
        catch(std::bad_alloc& ex)
        {
            std::cerr << ex.what() << std::endl;
        }
    }

    // Arithmetic shit
    bool    operator== (const Matrix &operand);
    bool    operator!= (const Matrix &operand);
    Matrix  operator+(const Matrix &operand);
};

#endif

matrix.cpp

#include <iostream>
#include "matrix.h"

/*  return 1 if ==
    return 0 if !=*/
bool Matrix::operator== (const Matrix &operand)
{
    if(operand.size != this->size)
        return 0;
    for(int i = 0; i < this->size; i++)
    {
        if(this->matrix[i][i] != operand.matrix[i][i])
            return 0;
    }
    return 1;
}

/*  return 1 if !=
    return 0 if ==*/
bool Matrix::operator!= (const Matrix &operand)
{
    if(operand.size != this->size)
        return 1;
    for(int i = 0; i < this->size; i++)
    {
        if(this->matrix[i][i] != operand.matrix[i][i])
            return 1;
    }
    return 0;
}

Matrix Matrix::operator+ (const Matrix &operand)
{
    const Matrix result;
    //pass
}

My question is about the addition operator. This method returns an object of the class. We can only add matrices of the same order. If, for example, matrices of a different order, or if I catch a bad memory allocation through an exception handler, then what should this method return if the operation cannot be performed?
nullptrwe cannot return.

Answer 1

1. There is no destructor in your code that would free memory => you have a potential memory leak.
2. In the case of the addition operator, if the matrices have different sizes, throw an exception through std::runtime_error
3. You do not have a copy constructor and when copying an object, a pointer to the allocated memory will be copied.