Abelian implies universal power map is endomorphism

Statement
Let $$(G, +)$$ be an Abelian group, and $$n$$ be an integer. The map $$g \mapsto ng$$ (i.e., the map $$g \mapsto g + g + \dots + g$$ done $$n$$ times when $$n$$ is positive and $$(-g) + (-g) + \dots + (-g)$$ done $$(-n)$$ times when $$n$$ is negative) is an endomorphism of $$G$$.

Proof
Given: An Abelian group $$G$$, an integer $$n$$.

To prove: The map $$g \mapsto ng$$ is an endomorphism of $$G$$: in other words, $$n(g + h) = ng + nh$$.

Proof: The proof basically follows from commutativity.