1. The problem statement, all variables and given/known data Let [itex]R[/itex] be a commutative ring with [itex]1[/itex]. What are the units of [itex]M_n(R)[/itex]? 2. Relevant equations N/A 3. The attempt at a solution If [itex]R[/itex] is a field, then I know that we can characterize the units as those matrices with non-zero determinant (since those are the invertible matrices). But since [itex]R[/itex] is not even an integral domain necessarily, I could use some help. Is there any nice way to characterize the units?