Solution to Exercise 3.23.
Definition of a Commonly Used Term in Math
 One May Show – One did, his name was Euclid.

Exercise 3.23. Show the group of affine transformations of the Euclidean plane is not commutative. 

One possible counterexample. Let

 and  

Then

 and  

Thus, AB does not equal BA. Hence, the group affine transformations of the Euclidean plane is not commutative under matrix multiplication.//