  We prove that for all integers $k \geq 1$, $q\ge (k-1)^4+ 6k$, and $m \geq
1$, every matrix in $ M_m(\mathbb F_q)$ is a sum of two kth powers:
$M_m(\mathbb F_q)=\{A^k+B^k|A,B\in M_m(\mathbb F_q)\}$. We further generalize
and refine this result in the cases when both $B$ and $C$ can be chosen to be
invertible, cyclic, or split semisimple, when $k$ is coprime to $p$, or when
$m$ is sufficiently large. We also give a criterion for the Waring problem in
terms of stabilizers.
