# Proof about identity element of a group

## Homework Statement

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

## 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.

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LCKurtz
Homework Helper
Gold Member
Hint: Think about using $b^{-1}$.

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

LCKurtz