Prove that if G is a group with the property that the square of every element is the identity, then G is Abelian. Thanks
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The hypothesis implies that $\displaystyle (ab)(ab) = e.$ Hence, $\displaystyle ab = b^{-1}a^{-1}$. SInce $\displaystyle b^{-1}=b$ and $\displaystyle a^{-1}=a$, we're done.
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