When you raise your right hand, the image 'appears' to raise it's left hand. So a transposition HAS taken place. However, it wasn't the mirror that did it, it was in your mind. Because we are roughly symmetrical about a vertical axis our mind assumes that the right hand of the image is really a left hand of a person who has turned around and is looking at us.

Trouble is, the more you try to decribe the phenomenon the more confusing it gets.

Bert.