# Math Help - Question on group mapping

1. ## Question on group mapping

I working on a problem I can do since I have done many of this forum. However, I don't understand the group mapping:

G is a group and we are mapping G to G by $g\to g^{-1}$.

How does this mapping work?

2. ## Re: Question on group mapping

Originally Posted by dwsmith
How does this mapping work?
I don't understand the exact meaning of your question. The mapping $\psi:G\to G$ , $\psi(g)=g^{-1}$ is well defined (for every $g\in G$ there exists its inverse $g^{-1}$ and it is unique). Besides, $\psi(ab)=(ab)^{-1}=b^{-1}a^{-1}=\psi(b)\psi(a)$ for all $a,b\in G$ .

3. ## Re: Question on group mapping

Originally Posted by FernandoRevilla
The mapping $\psi:G\to G$ , $\psi(g)=g^{-1}$