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Prove the following Proposition

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Prove the following Proposition:

On Z_n, both * and + are commutative and associative.

The identity for Z_n with * is [1] and the identity for + is [0].

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Infinite thanks.

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Please, see the attachment. The proof is given in all details.

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OTA

Prove the following Proposition:
On Z_n, both ⨀ and ⊕ are commutative and associative.
The identity for Z_n with ⨀ is [1] and the identity for ⊕ is [0].

Proof. Recall that Z_n is the set of residue classes modulo n. ...

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