Identity Function is Completely Multiplicative

Theorem
Let $I_{\Z_{>0}}: \Z_{>0} \to \Z_{>0}$ be the identity function:
 * $\forall n \in \Z_{>0}: I_{\Z_{>0}} \left({n}\right) = n$

Then $I_{\Z_{>0}}$ is completely multiplicative.

Proof

 * $\forall m, n \in \Z_{>0}: I_{\Z_{>0}} \left({m n}\right) = m n = I_{\Z_{>0}} \left({m}\right) I_{\Z_{>0}} \left({n}\right)$