Let $f:G\to G$ when $f=x^2$ if $f$ is homomorphism then $G$ is abelian group.
suppose $f$ is homomorphism so $f(xy)=f(x)f(y)$ $\forall x,y \in G$
then $xy=yx$
how to prove this sentence.
2026-03-25 06:08:26.1774418906
Homomorphism and abelian group.
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$(xy)^2=xyxy$ in general. But your function being a homomorphism gives us the equation $(xy)^2=f(xy)=f(x)f(y)=x^2y^2=xxyy$ for any $x,y\in G$. So that way we get xyxy=xxyy. Can you finish from here?