I have a multi-step problem that I'm unsure how to do. I'm given Let $\varphi:G\rightarrow G'$ be a homomorphism between groups $G$ and $G'$. I have to prove the following:
a)If $e$ is the identity element of $G$, then $\varphi(e)$ is the identity element of $G'$.
I'm sorry that I asked multiple things at once. I'm new to this. I did search for my questions, but nothing maybe what I was looking for. As for what I've tried: Let $\varphi:G\rightarrow G'$ be a homomorphism between groups $G$ and $G'$. Also, let $e$ be the identity element of $G$. Since $\varphi:G\rightarrow G'$ is a homomorphism between groups $G$ and $G'$, then by definition $\varphi(e)$ is the identity element of $G'$.
This doesn't feel right though. I feel like something is missing.