Consider the subset S = {(0,0), (1,1), (2,2), (3,3)} of Z4 × Z4. a. Prove that S is a subring of 74 x 74- b. Is S a commutative ring? Justify your answer. c. Is S a ring with identity? Justify your answer. d. Is S an integral domain? Prove or disprove. e. Is S a field? Prove or disprove.

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