class Matrix{
public:
    vector<vector<int> > a;
    Matrix operator+(const Matrix & A);
};
Matrix Matrix::operator+(const Matrix & A){
    Matrix B;
    for (int i = 0; i < A.a.size(); i++) {
        for (int j = 0; j< A.a[0].size(); j++) {
            B.a[i][j] = a[i][j] + A.a[i][j];
        }
    }
    return B;   
}

What's problem?