# Homework Help: Proof about identity element of a group

1. Sep 4, 2012

### hoopsmax25

1. The problem statement, all variables and given/known data
If G is a group, a is in G, and a*b=b for some b in G (* is a certain operation), prove that a is the identity element of G

2. Relevant equations

3. The attempt at a solution
I feel like you should assume a is not the identity element and eventually show that a= the identity. but im not sure how to show that.

2. Sep 4, 2012

### LCKurtz

Hint: Think about using $b^{-1}$.

3. Sep 4, 2012

### hoopsmax25

I thought about using the inverse of b but i'm not sure how to plug it in?

4. Sep 4, 2012

### LCKurtz

You don't "plug it in". You could try *-ing things with it.

5. Sep 4, 2012

### hoopsmax25

Could you do a*b*b-inverse=b*b-inverse? and go from there?