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 All Solutions of the Yang-Baxter-like Matrix Equation When $A^3 = A$ Mansour Saeed Ibrahim Adam,Jiu Ding,Qianglian Huang,Lanping Zhu Keywords:Yang-Baxter-like matrix equation; Diagonalizable matrix; Eigenvalue. Abstract: Let $A$ be a square matrix satisfying $A^3 = A$. We find all solutions of the Yang-Baxter matrix equation $AXA=XAX$, based on our previous result on all the solutions of the same equation for a matrix $A$ such that $A^2 = I$.