2. (a.) Consider [3]12 in Z12. Is [3]12 a zero divisor of Z12 and does [3]...

2. (a.) Consider [3]₁₂ in Z₁₂. Is [3]₁₂ a zero divisor of Z₁₂ and does [3] have a multiplicative inverse in Z₁₂? Justify your answer.

(b.) Prove that [3]₁₀ has a multiplicative inverse in Z₁₀ and determine the order of [3] in Z^x₁₀. Justify your answer.

(c.) Prove that [6]₈ is a nilpotent element of Z₈. Justify your answer.

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Expert Solution

Colby Messinger answered 1 year ago

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