ABSTRACT
Let A be a nilpotent matrix of index three and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a simplified matrix equation of the same type with A replaced by its Jordan form, whose Jordan blocks are at most . Then we obtain a system of matrix equations of smaller sizes to find all the commuting solutions of the original matrix equation.
Disclosure statement
No potential conflict of interest was reported by the authors.