Let G be a group. Prove that the function: $G→G, x→x^2$ is a group homomorphism if and only if G is an abelian group.

Question

Let G be a group. Prove that the function: $G→G, x→x^2$ is a group homomorphism if and only if G is an abelian group.

Is this the same as if $f:G→G$ is defined by $f(x) = x^2$ ?