Hint for Question 9: See if you can reason from ab = e, be 2 (1, ea 2 b to show that (12 = b2 = (:2. Call this element 7. and deduce that z commutes with all three of a, b, :2. Using the three equal-inns invnlving a, b, :3 again, show that a l = (3 ac 1. Using this versinn, see if you can deduce that a and a 1 have the same square. 9. * Suppose that G is a group with distinct non-identity elements a, b, c, satisfying ab = c, bc = a, and ca = b. Show that at = b4 = c* = idG