Matrix3f A = Matrix3f::Random(3,3), B; B << 0,1,0, 0,0,1, 1,0,0; cout << "At start, A = " << endl << A << endl; A *= B; cout << "After A *= B, A = " << endl << A << endl; A.applyOnTheRight(B); // equivalent to A *= B cout << "After applyOnTheRight, A = " << endl << A << endl;