Say I have a $\alpha: G \to H$.
- What do I have to do to prove that $\alpha$ is a homomorphism? I thought it was just show $\alpha(g_1g_2) = \alpha(g_1)\alpha(g_2)$. But someone told me today that I also have to show $\alpha(g^{-1}) = \alpha(g)^{-1}$. Is this the case and if so why?
- Why is $\alpha(g^{-1}) = \alpha(g)^{-1}$?