Suppose that G is a group in which $\displaystyle g^{-1}=g ~\forall g \in G$. Prove that $\displaystyle G$ is abelian.

So what I need to show is that, in addition to G satisfying closure, associativity, identity and inverse, $\displaystyle G$ also satisfies commutativity ($\displaystyle ab=ba, \forall a,b \in G)$ but I'm not sure how to get started.