Question

is a plane mirror laterally inverted?

Answer 1

Yes. The image from a plane mirror is laterally inverted.

When the light gets reflected from a plane mirror, a virtual image is formed on the plane mirror at a distance exactly at the same distance between the object and the mirror.

Now, since a plane mirror is flat, the light that falls on it perpendicular reflects back through the same path.

So, the light that comes form the left side of the object will reflect to the left side itself and vice versa.

Now, the image on the mirror seems to be such that it is placed by rotating the object 180 degrees.

Both of these combined gives a lateral inversion for the image.