  We prove that for all integers $k \geq 1$, there exists a constant $C_k$
depending only on $k$, such that for all $q > C_k$, and for $n = 1, 2$ every
matrix in $M_n(\mathbb{F}_q)$ is a sum of two $k$th powers and for all $n \geq
3$ every matrix in $M_n(\mathbb{F}_q)$ is a sum of at most three $k$th powers.
