(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

On the set G=R-{1/3} the following operation is defined:

*G: GxG arrow G

(x,y) arrow x*y=x+y-3xy

Show that (G,*) is an abelian group.

2. Relevant equations

To proove something is an abelian group:

The Associative Law need to hold true x*(y*x)=(x*y)*x

Neutral Element needs to be true e*x=x*e=x for all or any x E G

Inverse Elements x*x'=x'*x=e where x' is called the inverse element of x

Commutativity x*y=y*x

3. The attempt at a solution

I don't know how to solve this, especially with a set like this. Any Hints or Advice would be greatly appreciated

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# Homework Help: Abelian Group; what to do if the set is G=R-{1/3}?

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