# Alg7.16

Let G be a group such that (ab)2 = a2b2 for all $a,b\in G$. Prove G is abelian.
$abab=(ab)^2=a^2b^2 \Rightarrow a^{-1}(abab)b^{-1}=a^{-1}(a^2b^2)b^{-1} \Rightarrow ba=ab\,$
Therefore, every $a\in G$ commutes with every other element of the group.