Face mirror. Hold book so you can read it. Now turn it to 'show it to the mirror'. The book is reversed right-left. Because you turned the book right-left.

Try it again - read the book. Now turn it to the mirror, but this time flip it top-bottom. Now the mirror is showing it reversed top-to-bottom, but the letters are still on the correct side (right on right; left on left).

So mirrors Don't reverse left-right. The do whatever you tell them to do.