# Math Help - Abelian Group

1. ## Abelian Group

Prove that if G is a group with the property that the square of every element is the identity, then G is Abelian.

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2. The hypothesis implies that $(ab)(ab) = e.$ Hence, $ab = b^{-1}a^{-1}$. SInce $b^{-1}=b$ and $a^{-1}=a$, we're done.