  Let $F$ be a field. In this note we give a construction for a family of
maximal Mathieu subspaces (or Mathieu-Zhao subspaces) of the matrix algebras
$M_n(F)$ $(n\ge 2)$. As an application we also give a classification of Mathieu
subspaces of $M_2(F)$ under the condition that $F$ is algebraically closed.

Rings and Algebras