We completely determine those natural numbers $n$ for which the full matrix ring $M_n(F_2)$ and triangular $T_n(F_2)$ over two elements field $F_2$ are either n-torsion clean or almost clean, respectively. These results somewhat address settle a question, recently posed by Danchev-Matczuk in Contemp. Math. (2019) as well they supply more precise aspect nil-cleanness property of $n\times n$ all ...