The following code works.

class Matrix{

public:
vector<vector<int> > a;

Matrix & operator + (const Matrix &y) {

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

    return *this;
}

};