Mate No Matter What

If White is to play, can he always mate Black in 2 moves, regardless of the moves played before?

         White to play and mate in 2 moves.

         White to play and mate in 2 moves.


The first thing to notice is that since the last move was made by Black, either the king or the rook was moved and therefore Black cannot castle anymore. Now White plays Qa1 and no matter what is Black's next move, Qh8 gives check-mate.