A note on Potter's theorem for quasi-commutative matrices (Q1006031)

The authors discuss the converse of a theorem of \textit{H. S. A. Potter} [Am. Math. Mon. 57, 321--322 (1950; Zbl 0040.00501)] stating that if a matrix equation \(AB=\omega BA\) is satisfied with \(\omega\) a primitive \(q\)th root of unity, then \(A^q+B^q=(A+B)^q\). They modify both conditions in order to get a converse and they present a characterization when the converse holds for these modified conditions and \(q=3\), and a conjecture for the general case.