How to prove that for each $n> 0$, $\mathrm{Mat}_n(R)$ is a ring?

How to prove that for each $n> 0$, $\mathrm{Mat}_n(R)$ is a ring?

How to prove that for each $n> 0$, $\mathrm{Mat}_n(R)$ is a ring? and that
if $R$ has an identity, so does $\mathrm{Mat}_n(R)$ (namely the identity
matrix $I_n$).
Note: The set of all $n \times n$ matrices over R is denoted as
$\mathrm{Mat}_n(R)$.