That is correct, in case anyone wants a implementation thas does not modify:

class Matrix{

public:
vector<vector<int> > a;

Matrix operator +(const Matrix &y){
    Matrix res;

    for(int m=0; m<y.a.size(); ++m){
        vector<int> z;
        for(int n=0; n<y.a[0].size(); ++n){
            int num = (this->a[m][n] + y.a[m][n]);
            z.push_back(num);
        }
        res.a.push_back(z);
    }

    return res;
}

};