D. Given the set F= {0, a, b, c, d} with operations + and * and the following tables, assume that Fwith these operations is a ring with additive identity 0. Оа bc d Оa b c d 0 a bc d 00 0 0 0 0 b c d + d 0 b c d 0 a cd 0 a b d|d0 a bc 0 a b o b d a co c a a b a b a d b d|o d c b a Using the information about set F, do the following: 1. Prove that Fis a field, using these operations, by doing the following: a. Prove the commutative property of * b. Prove there is an identity for F under the operation * c. Prove each nonzero element is a unit of Funder the operation *.

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