A division ring is a (not necessarily commutative) ring R with identity 1R # 0p that satisfies Axioms 11 and 12 (pages 48 and 49). Thus a field is a commutative division ring. See Exercise 43 for a noncommutative example. Suppose R is a division ring and a, b are nonzero elements of R. (a) If bb = b, prove that b = 1p. [Hint: Let u be the solution of bx = Ip and note that bu = b}v.] (b) If u is the solution of the equation ax = 1r, prove that is also a solution of the equation xa = 1p. (Remember that R may not be commutative.) [Hint: Use not (a) with b = wal