Jacobson radical of matrix ring

Question

Let $R$ be a ring, $S$ be the subring of matrix ring $M_2(R)$ consisting of upper triangular matrices $\left( \begin{matrix} a& b\\ 0& d\\ \end{matrix} \right)$ with $a,b,d\in R$, how to prove that

1. $J(M_n(R))=M_n(J(R))$;

2. $J(S)$ consists of matrices $\left( \begin{matrix} a& b\\ 0& d\\ \end{matrix} \right)$ with $a,d\in J(R)$ and $b\in R$?

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For the first problem, we know that $$A\in J(M_n(R))\Longleftrightarrow AB=0, \text{for every simple left $M_n(R)$-mdule $B$.}$$

I want to show that all entries of $A$ are in $J(R)$, but i do not know what to do with "simple left $M_n(R)$-module $B$".

Thanks for your help.