Let $G=Spec(A)$ be an affine group scheme over $Spec(k)$ with $k$ a field. The neutral of $G$ is an element $e\in |G|$, which is the image of the zero ideal by the continuous map: $|Spec(k)|\rightarrow |G|$. Let write it $e:=p \in Spec(A)$
Let have a look at $G\times G$. This is also a $k$-affine scheme, $G\times G=Spec(A\otimes A)$. I am looking for its neutral element. As above, it is the image of the zero ideal by the continuous map: $|Spec(k)|\rightarrow |G\times G|$.
What is it ? I don't know how to find it.