Let the Jordan canonical form of a 3 × 3 matrix A be J = diag (J₂ λ, J₁ µ), where λ ≠ 0 and µ ≠ 0. We find all the solutions of the Yang-Baxter-like matrix equation AXA = XAX successfully by discussing whether λ and µ are equal.
Li et al. (Wed,) studied this question.