Isometries, math homework help

Demonstrate, using a counter example, that the product of a pair of isometries A and B is not always commutative (i.e., AB does not always equal BA).

Suppose A1 is a reflection with mirror m1 and A2 is a reflection with mirror m2, and suppose that m1 and m2 are not parallel. Let O be the intersection point of m1 and m2, and let x be the measure of the angle from m1 to m2. Then A2A1 is rotation with center O and angle measure 2x, but A1A2 is rotation with center O and angle measure -2x.

This was an answer I gave to the title question, was asked for a more specific answer