In the Euclidean plane, we have the following possibilities.
*; [  ] Identity
:Two reflections in the same mirror restore each point to its original position. All points are left fixed. Any pair of identical mirrors has the same effect.
*; [] Reflection
:As Alice found through the looking-glass, a single mirror causes left and right hands to switch. (In formal terms, topological orientation is reversed.) Points on the mirror are left fixed. Each mirror has a unique effect.
*; [] Rotation
:Two distinct intersecting mirrors have a single point in common, which remains fixed. All other points rotate around it by twice the angle between the mirrors. Any two mirrors with the same fixed point and same angle give the same rotation, so long as they are used in the correct order.
*; [] Translation
:Two distinct mirrors that do not intersect must be parallel. Every point moves the same amount, twice the distance between the mirrors, and in the same direction. No points are left fixed. Any two mirrors with the same parallel direction and the same distance apart give the same translation, so long as they are used in the correct order.
*; [] Glide reflection
:Three mirrors. If they are all parallel, the effect is the same as a single mirror (slide a pair to cancel the third). Otherwise we can find an equivalent arrangement where two are parallel and the third is perpendicular to them. The effect is a reflection combined with a translation parallel to the mirror. No points are left fixed.