Given that $f:G\to G$ on a group $G$, defined by $f(x)=x^3$, is an isomorphism, how do I show that $G$ is abelian? Given that $f:G\to G$ on a group $G$, defined by $f(x)=x^3$, is an isomorphism, how do I show that $G$ is abelian, please?

Answer of the changed question: Note that for any $a,b \in G$, $xy=f(x^{-1})f(y^{-1})=f(x^{-1}y^{-1})=f((yx)^{-1})=yx$.Hence $G$ is abelian.
