# Group problem

1. Dec 17, 2013

### LagrangeEuler

1. The problem statement, all variables and given/known data
Find $(g_ig_j)^{-1}$ for any two elements of group $G$.

2. Relevant equations
For matrices $(AB)^{-1}=B^{-1}A^{-1}$

3. The attempt at a solution
I'm not sure how to show this? I could show that for matrices $(AB)^{-1}=B^{-1}A^{-1}$. And that for numbers
$(ab)^{-1}=a^{-1}b^{-1}$

2. Dec 17, 2013

### tiny-tim

Hi LagrangeEuler!
If h = $(g_ig_j)^{-1}$, then $hg_ig_j$ = I.

Sooo what combinations of gs would h have to be made of?

3. Dec 17, 2013

### LagrangeEuler

Could I just write from that relation that $(g_ig_j)^{-1}=g_j^{-1}g_i^{-1}$? :)
It looks obvious but what is right mathematical way to write it? :)

4. Dec 17, 2013

### jbunniii

Check whether it satisfies the properties of the inverse. If $h$ is the inverse of $g$, then $hg = gh = 1$. See if your $h$ satisfies this for $g = g_i g_j$.