(adsbygoogle = window.adsbygoogle || []).push({}); Group Inverse--Seems to easy, please check!

Hi all, this just seems too easy, and my teacher is prone to typos... I was thinking perhaps it was one.

1. The problem statement, all variables and given/known data

Prove that for a group G there exists a unique element that satisfies the equation x * x = x.

2. The attempt at a solution

Multiplying both sides by the inverse, x^{-1}, we have

x^{-1} * x * x = x^{-1} * x => (x^{-1} * x) * x = x^{-1} * x => e * x = e => x = e

and we see that for this relation to hold, x must be the identity element, which is unique.

Thanks in advance!

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# Group Inverse-Seems to easy, please check!

**Physics Forums | Science Articles, Homework Help, Discussion**