Explicit solutions of the Yang-Baxter-like matrix equation for a singular diagonalizable matrix with three distinct eigenvalues

Let A be a singular diagonalizable complex matrix with three distinct eigenvalues. We derive all explicit solutions X of the Yang-Baxter-like equation AXA = XAX, by taking advantage Jordan form structure A. The result generates formula obtained in Chen et al. (2019) and M. Saeed Ibrahim Adam (2019). give examples to illustrate validity results this paper.