I have question about exercise module theory in Hartley's book.
Find a natural way of making $M_n(R)$ into an $R$-module, and show that then $M_n(R)\cong {}_RR\oplus\ldots\oplus{}_RR$, the external direct sum of ${}_RR$ with itself $n^2$ times.
My question:
(1) What the meaning of "find a natural way"?
(2) To prove $M_n(R)\cong {}_RR\oplus\ldots\oplus{}_RR$, it must be shown that there exist an isomorphism between $M_n(R)$ and ${}_RR\oplus\ldots\oplus{}_RR$. How to define the mapping for this problem such that it can be an isomorphism?