## Group Homomorphism Sends the Inverse Element to the Inverse Element

## Problem 444

Let $G, G’$ be groups. Let $\phi:G\to G’$ be a group homomorphism.

Then prove that for any element $g\in G$, we have

\[\phi(g^{-1})=\phi(g)^{-1}.\]

Let $G, G’$ be groups. Let $\phi:G\to G’$ be a group homomorphism.

Then prove that for any element $g\in G$, we have

\[\phi(g^{-1})=\phi(g)^{-1}.\]