If $(G,*)$ is a group and $a^{-1}=a, \forall a \in G$ then $G$ is abelian .

Question

If $(G,*)$ is a group and $a^{-1}=a, \forall a \in G$ then $G$ is abelian . Is it true or false and why?

Welcome to stackexchange. Your question has been downvoted because you didn't provide any information about how you got started and where you were stuck. You did get answers anyway - but next time please ask your question better. Note too that someone edited to improve the math formatting. Do that yourself next time. — Ethan Bolker, Nov 15 '17 at 14:04

score 1 · Answer 1 · answered Nov 15 '17 at 14:01

1

HINT: Take $a = xy$ for any $x,y \in G$

answered Nov 15 '17 at 14:01

Stefan4024

1

A brief remark of this kind is more appropriately offered as a Comment. – hardmath Nov 15 '17 at 14:02
@hardmath You can say so and that's why I put the hint label in front. I usualy tend to do this when I believe a hint will do the job – Stefan4024 Nov 15 '17 at 14:04

score 1 · Accepted Answer · answered Nov 15 '17 at 14:02

1

It is true. We have $abab=e$ then $ab=b^{-1}a^{-1}$ but $b^{-1}a^{-1}=ba$

answered Nov 15 '17 at 14:02

GhD

2 Answers2