# Homework Help: Abstract Abgebra proof

1. Jul 20, 2010

### stihl29

Let G be a group. Show (xy)$$^{-1}$$ = x$$^{-1}$$y$$^{-1}$$ for all x, g $$\in$$ G if and only if G is abelian.

2. Relevant equations

3. The attempt at a solution

2. Jul 20, 2010

### gomunkul51

I think you're done :)

3. Jul 20, 2010

### Staff: Mentor

What have you tried?

4. Jul 20, 2010

### hunt_mat

The element $$(xy)^{-1}$$ is the inverse element of $$xy$$ and therefore $$(xy)^{-1}xy=e$$ where e is the identity, so...