  A ring $R$ is trinil clean if every element in $R$ is the sum of a tripotent
and a nilpotent. If $R$ is a 2-primal strongly 2-nil-clean ring, we prove that
$M_n(R)$ is trinil clean for all $n\in {\Bbb N}$. Furthermore, we show that the
matrix ring over a strongly 2-nil-clean ring of bounded index is trinil clean.
We thereby provide various type of rings over which every matrix is the sum of
a tripotent and a nilpotent.
