1. The problem statement, all variables and given/known data I need to prove or disprove this statement: "If all eigenvalues of a diagonalizable matrix A are equal and have the same value c, then A=cI." 2. Relevant equations 3. The attempt at a solution I have tried coming up with a diagonalizable matrix that has eigenvalues with all the same value, but so far the only ones I can come up with are ones that fit A=cI. In other words, I can't disprove it. However....I have no idea how to prove it is true either!