This is the shape that results when Black captures a stone. Can White play at A?



If White tries to play here, as on the right, White 1 doesn't have any liberties, so it is captured. Since captured stones are taken off the board, it looks like White didn't play but just gave Black a stone. You can't put a stone on a point without liberties.

Black 1 is not the same as White 1. Black 1 is connected to the other Black stones and shares liberties with them.

Can White play 1?

White can play 1 because White's stone has a liberty at A. (Black can capture White 1 easily by playing at A, so White 1 isn't a great move, but it still remains on the board.

How about White 1 here?

This point has no liberties, so White cannot put a stone here.