Identity Function is Completely Multiplicative

Theorem
Let $I_{\Z^*_+}: \Z^*_+ \to \Z^*_+$ be the identity function:
 * $\forall n \in \Z^*_+: I_{\Z^*_+} \left({n}\right) = n$

Then $I_{\Z^*_+}$ is completely multiplicative.

Proof

 * $\forall m, n \in \Z^*_+: I_{\Z^*_+} \left({m n}\right) = m n = I_{\Z^*_+} \left({m}\right) I_{\Z^*_+} \left({n}\right)$