IMC 2015 Problem 9

An $n \times n$ complex matrix $A$ is called \emph{t-normal} if $AA^t = A^t A$ where $A^t$ is the transpose of $A$ . For each $n$ , determine the maximum dimension of a linear space of complex $n \times n$ matrices consisting of t-normal matrices.

Proposed by Shachar Carmeli, Weizmann Institute of Science