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Benzoate

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## Homework Statement

Prove that if (ab)^2=a^2*b^2, in a group G, then ab =ba

## Homework Equations

No equations necessary for this proof

## The Attempt at a Solution

Suppose (ab)^2=a^2*b^2. Then (ab)^2=(ab)(ab)=(abba)=(ab^2*a)=a^2 *b^2=> (ab)(ba)=(ba)(ab) = e

By cancellation, (ab)=(ba) <=> (ba)=(ab)

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