RO-NMO 2017 Problem 113

Let be a natural number $n\ge 2$ and two $n\times n$ complex matrices $A,B$ that satisfy $(AB)^3=O_n.$ Does this imply that $(BA)^3=O_n ?$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.