SOLUTION: Demonstrate, using a counter example, that the product of two isometries P and Q is not always commutative (i.e., PQ does not always equal QP).
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Question 1103091: Demonstrate, using a counter example, that the product of two isometries P and Q is not always commutative (i.e., PQ does not always equal QP). Answer by ikleyn(52788) (Show Source):
You can easily do it on your own by taking the parallel translation on 1 unit to the righ as an isometrie P on the 2D coordinate plane
and taking the rotation to the angle 90 degs anticlockwise as an isometrie Q of the same 2D coordinate plane.
Then consider the image of the point (x,y) = (1,0) under PQ and under QP.
