Group Theory Help: Show (x*y*z^-1)^-1 = x*y^-1*z^-1

[Seb97]

Homework Statement

Let G(*) be a group.
If x.y are elements of G show that (x*y*z^-1)^-1 = x*y^-1*x^-1

Homework Equations

The Attempt at a Solution

I first took the left side of the equation and computed the inverse and I got x^-1*y^-1*z
I then let this equal to the righthand side and concluded since the elements are in a group the associativity law holds they are equal. I was just wondering is this valid or am I missing something.

 

[JSuarez]

I think the right side should be zy^-1x^-1, not xy^-1x^-1.