I wanted to implement the strassen's algorithm and I though to implement a matrix class. However I get a segmentation fault with the following code:
class Matrix {
    public:
        vector < vector <int> > m;
        int r;
        int c;
        Matrix() {;}
        Matrix(int _r, int _c) {
            r = _r;
            c = _c;
            m.resize(r);
            for (int i = 0; i < r; i++) {
                m[i].resize(c);
            }
            for(int i =0; i < r; i++){
                for(int j=0; j< c; j++){
                    m[i][j] = 0;
                }
            }
        }
        friend ostream& operator<<(ostream &out, Matrix &A) {
            for(int i =0; i<A.r; i++){
                out << endl;
                for(int j=0; j<A.c; j++){
                    out << A.m[i][j] << "\t";
                }
            }
            out<< endl;
            return out;
        }
        Matrix(const Matrix &A) {
            c = A.c; 
            r = A.r;
            m.resize(r);
            for (int i = 0; i < r; i++) {
                m[i].resize(c);
            }
            for(int i =0; i<r; i++){
                for(int j=0; j<c; j++){
                    m[i][j] =  A.m[i][j];
                }
            }
        }
        Matrix& operator-= (Matrix &A) {
            assert(A.r == r);
            assert(A.c == c);
            for(int i =0; i<r; i++){
                for(int j=0; j<c; j++){
                    m[i][j] -= A.m[i][j];
                }
            }
            return *this;
        }
        Matrix& operator- (Matrix &A) {
            Matrix C(*this);
            return C-=A;
        }
        Matrix& operator+= (Matrix &A) {
            assert(A.r == r);
            assert(A.c == c);
            for(int i =0; i<r; i++){
                for(int j=0; j<c; j++){
                    m[i][j] += A.m[i][j];
                }
            }
            return *this;
        }
        Matrix& operator+ (Matrix &A) {
            Matrix C (*this);
            (C)+=A;
            return C;
        }
        Matrix getBlock(int sR, int eR, int sC, int eC) {
            assert(sR > eR);
            assert(sC > eC);
            Matrix C(eR-sR, eC-sC);
            for(int i = 0; i < C.r; i++) {
                for(int j=0; j < C.c; j++) {
                    C.m[i][j] = m[sR+i][sC+j];
                }
            }
            return C;
        }
        friend void swap(Matrix& first, Matrix& second) {
            using std::swap; 
            swap(first.r, second.r); 
            swap(first.c, second.c); 
            swap(first.m, second.m);
        }
        Matrix& operator=(Matrix other){
            return *this;
        }
        friend Matrix& operator*(const Matrix& A, const Matrix &B) {
            assert(A.r == B.c);
            Matrix C(A.r, B.c);
            for(int i =0; i<C.r; i++){
                for(int j=0; j<C.c; j++){
                    for(int k = 0; k < A.r; k++) {
                        C.m[i][j] += A.m[i][k] * B.m[k][j];
                    }
                }
            }
            return C;
        }
};
int main (void) 
{
    Matrix A(2,2), B(2,2);
    A.m[0][0] = 1;  A.m[0][1] = 2;
    A.m[1][0] = 3;  A.m[1][1] = 4;
    B.m[0][0] = 1;  B.m[0][1] = 2;
    B.m[1][0] = 3;  B.m[1][1] = 4;
    Matrix C(2,2);
    C =A+B;
    cout << C << endl;
    return 0;
}
If I try A+=B; it works... I do not understand what it is the difference with A+B. I tried to print C before returning from
Matrix& operator+ (Matrix &
    Matrix C (*this);
    (C)+=A;
    return C;
} 
And it is correct. When the code hit the return, my program crashes. I would like to understand what I am doing wrong. Thanks a lot. Davide
 
     
     
    