Matrix Waring Problem. II

We prove that for all integers k ≥ 1, there exists a constant C_k depending only on k such that for all q > C_k and for all n ≥ 1 every matrix in \(M_{n}({\mathbb F}_{q})\) $$M_n({\mathbb{F}}_q)$$ is a sum of two kth powers.