I've read something about it some days ago, here's the possible conclusion:
Look in the mirror.
Point to your left, and your reflection points to your left. Point to your right and your reflection points to your right.
I've just proven the mirror does nothing to the x axis.
Point up, and your reflection points up. Point down, and your reflection points down.
I've just proven the mirror does nothing to the y axis.
Point to your forward and your reflection points in the direction behind you.
Point to your reverse and your reflection points to your forward.
I've just proven the mirror reverses the z axis.
You have no ground to stand on disagreeing with any of this.