2.7. If G is a group such that (ab)2 = a2b2 for all a, b ∈ G, then show that G must be abelian.
abab=a2b2abab=a^2b^2abab=a2b2 apply a−1a^{-1}a−1 from left and b−1b^{-1}b−1 from right. We obtain ba=abba=abba=ab for all a,b∈Ga,b\in Ga,b∈G. Hence GGG is abelian.
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