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