  We investigate properties of group gradings on matrix rings $M_n(R)$, where
$R$ is an associative unital ring and $n$ is a positive integer. More
precisely, we introduce very good gradings and show that any very good grading
on $M_n(R)$ is necessarily epsilon-strong. We also identify a condition that is
sufficient to guarantee that $M_n(R)$ is an epsilon-crossed product, i.e.
isomorphic to a crossed product associated with a unital twisted partial
action. In the case where $R$ has IBN, we are able to provide a
characterization of when $M_n(R)$ is an epsilon-crossed product. Our results
are illustrated by several examples.
