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.
Question 19.99
69. 
Show that successive tire rotations using scheme A form a group. Is it the Klein 4-group (page 805)?
69.
Answers will vary. No, it is the cyclic group of order 4—e.g., the tire at position 1 goes to 3, then to 2, then to 4, and then back to 1.