A group $G$ is Abelian iff $(ab)^n = a^n b^n$ for all $a,b \in G$ and $n \in \Bbb Z$ 
Prove that $G$ is Abelian if and only if $(ab)^n =a^n b^n $ for all $a, b \in G$ and $ n \in \mathbb{Z} $.

I used proof by induction in the $ \rightarrow$ direction of the proof and I'm done with that. 
Any help/hint on the $ \leftarrow$ direction.

It should read "...for all $a,b\in G$ and $n\in\Bbb Z$."
Take $n=2$ and you get $abab= aabb$. Now use inverses.
