Let $p$ be a prime and $q=p^n$. Let $\mathbb F_{q^2}$ be a field with $q^2$ elements and $\sigma$ its authomorhism of order two. A $m$ by $m$ matrix $A$ over $\mathbb F_{q^2}$ is hermitian if $A^\sigma$ coincides with the traspose of $A$.
Do you know a reference to the following result?
Theorem. The ring of $m$ by $m$ matrices over $\mathbb F_{q^2}$ can be generated over $\mathbb F_p$ by two hermitian matrices.
