  In order to find a suitable expression of an arbitrary square matrix over an
arbitrary finite commutative ring, we prove that every such a matrix is always
representable as a sum of a potent matrix and a nilpotent matrix of order at
most two when the Jacobson radical of the ring has zero-square. This somewhat
extends results of ours in Lin. & Multilin. Algebra (2021) established for
matrices considered on arbitrary fields. Our main theorem also improves on
recent results due to Abyzov et al. in Mat. Zametki (2017), \v{S}ter in Lin.
Algebra & Appl. (2018) and Shitov in Indag. Math. (2019).
