Mapping to Square is Endomorphism iff Abelian

Theorem
Let $$\left({G, \circ}\right)$$ be a group.

Let $$\phi: G \to G$$ be defined such that $$\forall g \in G: \phi \left({g}\right) = g \circ g$$.

Then $$\left({G, \circ}\right)$$ is abelian iff $$\phi$$ is an endomorphism.