Question: Please help me on proving this question. Explanation would also be really helpful. Thanks ? 2.5.46. Let F = {0, 1, a, b} be a

Please help me on proving this question. Explanation would also be really helpful. Thanks

2.5.46. Let F = {0, 1, a, b} be a eld with four elements. (a) Prove that a2 = b, and that b:2 = a. (b) What are a3 and b3? (c) (Harder!) Prove that 1 + 1 = 0. (Hint: Assume that 1+1 = a. What does that imply about 1+a and 1+b? Show that the assumption leads to a2 = 0, which is impossible.)

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