But if we were applying the transforms in reverse order (as we need to for the inverse identity above): T^-1 * M^-1 [1 0 0] [A B 0] [A B 0] where [X' Y'] = [X Y] * [A B] [0 1 0] * [C D 0] = [C D 0] [C D] [X Y 1] [0 0 1] [X' Y' 1]