- #1
lostinmath08
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Homework Statement
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.
Homework 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
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