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Math · Advanced Math
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1. A square matrix N is called nilpotent if N 0 for some positive integer m. (a) Is the sum of two nilpotent matrices nilpotent? If yes, prove it. If not, give a counter example. (b) Is the product of two nilpotent matrices nilpotent? If yes, prove it. If not, give a counterexample. (c) Prove that all eigenvalues of a nilpotent matrix are zero (d) Prove that the only nilpotent matrix that is diagonalizable is the zero matrix.
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