Mirror and its properties

Nope!

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Mirror only changes direction that is parallel to the normal of its surface.
Let me demostrate with this picture:

In this image, the top arrows, which is parallel to the normal, and perpenticular to the mirror's surface, is perfectly inflected.
The bottom arrows, which is perpenticular to the normal, is not inflected at all.
You can imagine a slanted line, like \\, will be turned into /

If you hold a piece of paper parrallel to the surface of the mirror, none of the paper, nor the letter which is printed on the paper, will be parrallel to the normal vector of the mirror.
See image:

Think of the paper as an infinite set of vectors, each of them perpenticular to the normal.

So now we think to ourselves:
If the mirror only reflects what is parallel to the normal, and the paper hold in front of the mirror has nothing in parallel to the normal, what caused the letters to flip over?

The answer is: whatever caused the letters to flip over is NOT the mirror.

In fact, what made the letters flip over is the way we positioned the paper in front of the mirror.
The case becomes easier to understand if we use a set of transparent papers to show what happens.
See images:


So it is not the mirror that flipped the image, it is entirely depended on the way we flip the paper over.

Here is how you would inverted 2 kinds of letters.

Letter B, which is symmetrical from top to down but not from left to right, will become inverted in mirror if you flip it along a vertical axis, which will switch its left and right.
Letter W, which is symmetrical from left to right but not from up to down, will become inverted in mirror if you flip it along a horizontal axis, which will switch its up and down.