If field $K$ splits $S$, a central simple algebra over field $k \subset K$, then $K' \supset K$ splits $S$.

Question

I want to prove the following.

If field $K$ splits $S$, a central simple algebra over field $k \subset K$, then $K' \supset K$ splits $S$.

$K$ splits $S$ means $K \otimes_{k} S \cong_{K}M_n(K) $. We take tensor by $K'$ to get $$K' \otimes _{K}K \otimes _{k} S \cong _{K} K' \otimes_K M_n(K) $$
This gives us $$ K' \otimes_kS \cong_K M_n(K') $$
The only problem is to say that $K'$ splits $S$ we need $K'$ algebra isomorphism in above equation. How do we get that ?