# Homomorphism of groups

1. Dec 12, 2013

### LagrangeEuler

1. The problem statement, all variables and given/known data
Show that
$f(e)=e'$ and $f(g^-1)=f(g)^-1$

2. Relevant equations
Homomorphism
f(x\cdot y)=f(x)\cdot f(y)

3. The attempt at a solution
I show the first one. Neutral element is element which satisfied
$e\cdot e=e$.
So
$f(e)=f(e\cdot e=e)=f(e)\cdot f(e)$
So $f(e)=e'$.
But how to show
$f(g^{-1})=f(g)^{-1}$?

2. Dec 12, 2013

### pasmith

What is $f(gg^{-1})$?

3. Dec 12, 2013

Tnx.