Let $\displaystyle R$ be a commutative ring with 1. Characterize the units of $\displaystyle M_n(R)$.

If $\displaystyle R$ is a field, then the usual characterization of the units are those matrices with non-zero determinant. But since $\displaystyle R$ is just a commutative ring with 1 (and not even an integral domain) I have no idea how to characterization the units. Is there any nice way to do this?