Question: The even integers 2Z form a ring with the usual operations of integer addition and multiplication. Given this fact, you are asked to prove that

The even integers 2Z form a ring with the usual operations of integer addition and multiplication. Given this fact, you are asked to prove that M(2Z) also has properties of a ring in part A. Each step of each proof must be justified using the definitions of the operations or an appropriate property from the even integers. The proofs of multiplicative closure (property 2) and associativity of multiplication (property 6) are provided for reference in the attached document "Proof of properties 2 and 6.&quot

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