Let baec398d93cf2051e4b7a7c7c2f97" title="Click to view the MathML source">A be an idempotent matrix. We obtain an explicit expression for all the solutions of the quadratic matrix equation AXA=XAX, completing the task of finding general solutions of the equation explicitly with a given idempotent matrix baec398d93cf2051e4b7a7c7c2f97" title="Click to view the MathML source">A.