Please give me some hint to solve this problem. dont give me final answer let me trying to solve this. Thank you so much
\begin{array}{l}{\text {Let } T=M_{n \times n}(R) . \text { Set }} \\ {S=\left\{E_{ij} | 1 \leq i, j \leq n\right\} \cup\{0\}} \\ {\text { Show } S \text { is closed under multiplication in } T .}\end{array}
Hint: The (a, b)-th entry of $E_{ij}E_{kl}$ is $\sum_{r=1}^n E_{ar}E_{rb}$. Now use the definition of $E_{ij}$.