This question has been asked numerous times on AB. Fact is, the mirror doesn't reverse anything. To prove this, simply stand in front of the mirror and extend either hand to touch the mirror. The reflected image you are touching is exactly the same... i.e., your left hand touches the left hand reflected in the mirror. The reflected light from you reflects directly back so their is no reversion...
as explained previously, a mirror doesnt reverse horizontally, it reverses back to front ( assuming you are facing it ) . In maths, it would be called a reflection witch plane is the mirror's plane.
Like many difficult questions the answer is that the question is wrong! In this case we expect to see an image of ourselves as if rotated about a vertical axis in front of us. If you want to see such an image try placing two mirrors at right angles like the corner of a room. I have always wanted to make a bathroom mirror like this and then see what happens when someone tries to put make up on or shave using it!