Very good gradings on matrix rings are epsilon-strong

We investigate properties of group gradings on matrix rings Mn(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 Mn(R) is necessarily epsilon-strong. We also identify a condition that is sufficient to guarantee that Mn(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 provide a characterization of when Mn(R) is an epsilon-crossed product. Our results are illustrated by several examples.