if G is generated by {a,b} and ab=ba, then prove G is Abelian if G is generated by {a,b} and ab=ba, then prove G is Abelian
All elements of G will be of the form $a^kb^j,\,\, k,j \in \mathbb{Z}^+$ 
so I need to get $a^kb^j = b^ja^k$

Other than induction you can try this. The center of $G$ name it $Z(G)$ contains $\{a,b\}$ the generators of the grup $G$ and also it is generated by them. Also $Z(G)\leq G$ ,thus $Z(G)=G$. This means that $G$ is abelian.
