Group Property of element

Question

True or false? If $G$ is a group with the property that $g=g^{-1}$ for all g element $G$, then $G$ is abelian .prove

true ,inverse exits which is in G,for it to be abelian ,it means that it is commutative that is $ab=ba$

Please try the search first next time. There are already a handful of posts on this question. — rschwieb, Sep 08 '14 at 10:34

score 2 · Answer 1 · answered Sep 08 '14 at 07:13

2

Let $a,b\in G$ then

$$ab=(ab)^{-1}=b^{-1}a^{-1}=ba$$ and we conclude.

answered Sep 08 '14 at 07:13

1 Answers1