Solve these algebraic problems

35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. Let F be a eld of order 2". Prove that char F = 2. Determine all elements of an integral domain that are their own inverses under multiplication. Characterize those integral domains for which 1 is the only ele ment that is its own multiplicative inverse. Determine all integers n > 1 for which (n I)! is a zero-divisor in Z\". Suppose that a and I; belong to an integral domain. a. If a5 = b5 and a3 = 133, prove that a = b. b. If am = I)\" and a" = b\