I have $M$ a left module over $R$. I take $M^{(n)}$ the direct sum of $n$ copies of $M$. Then $A := _R\text{End}(M^{(n)})$ is exactly the ring of $n\times n$ matrices with entries in $E:= _R\text{End}(M)$.
Why is this true?
It is clear that given a matrice, it is in $A$ but why, given $f\in E$ is it necessarily a matrice?