I am trying to show the following statement.
Assume $k$ is an algebraically closed field. Let $R$ be a $k$-algebra $R$. Then, $R$ is an integral $k$-algebra if and only if $R$ is a geometrically integral $k$-algebra.
Definition: We say that a ring $R$ is an integral $k$-algebra if it is a $k$-algebra that is an integral domain. We say that a ring $R$ is an geometrically integral $k$-algebra if it is a $k$-algebra such that for every field extension $k'\supset k$, the ring $R\otimes_{k}k'$ is an integral $k'$-algebra.
"if"-part is trivial but I don't know how to prove "only if"-part. In fact, this is an exercise problem in the algebra class (not algebraic geometry) so I just know the basic definition of tensor product.
Thanks in advance!