Prove that the set R= Z m of residue classes modulo a positive integer m, with respect

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Question:

Prove that the set R= Z_m of residue classes modulo a positive integer m, with respect to addition and multiplication of residue classes, is a commutative ring with identity. Show also that this ring is an integral domain if and only if m is a prime number. What will happen when m is a composite number, say 6?