Group with Zero Element is Trivial

Theorem
If a group $$\left({G, \circ}\right)$$ has a zero element, then $$\left({G, \circ}\right)$$ is the Trivial Group.

Proof
Let $$z \in G$$ be a zero element, and $$e \in G$$ be the identity element of $$G$$.

Let $$x \in G$$ be any arbitrary element of $$\left({G, \circ}\right)$$.

Then:

$$ $$ $$ $$ $$

So whatever $$x \in G$$ is, it has to be the identity element of $$G$$.

So $$G$$ can contain only that one element, and is therefore the Trivial Group.