  We completely determine those natural numbers $n$ for which the full matrix
ring $M_n(F_2)$ and the triangular matrix ring $T_n(F_2)$ over the two elements
field $F_2$ are either n-torsion clean or are almost n-torsion clean,
respectively. These results somewhat address and settle a question, recently
posed by Danchev-Matczuk in Contemp. Math. (2019) as well as they supply in a
more precise aspect the nil-cleanness property of the full matrix $n\times n$
ring $M_n(F_2)$ for all naturals $n \geq 1$, established in Linear Algebra and
Appl. (2013) by Breaz-Calugareanu-Danchev-Micu and again in Linear Algebra &
Appl. (2018) by Ster as well as in Indag. Math. (2020) by Shitov.
