For Exercises 69–72, refer to the following. Like mattresses, car tires need to be rotated so as to promote even wear; wear on a tire varies with wheel position. The three main rotation schemes are shown below.

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Question 19.102

72. Do the five tire rotation schemes A, B, C, D, and E, plus the identity rotation and any others that you found in Exercise 69, form a group? Why or why not?