Let $G$ be an affine group scheme of finite type over an algebraically closed field $k$. Suppose that $V$ is a finite dimensional representation of $G$.

Definition. $V$ is absolutely irreducible if for every $k$-algebra $A$ the representation $V_A = V\otimes_kA$ of the group $G_A = \mathrm{Spec}\, A\times_{\mathrm{Spec}\,k}G$ is irreducible (there are no $G_A$-stable $A$-submodules of $V_A$).

I think that I can prove the following result.

Suppose that $G$ is reduced. If $V$ is irreducible, then $V$ is absolutely irreducible.

Now my question:

Suppose that $G$ is nonreduced. If $V$ is irreducible, then is $V$ absolutely irreducible?