Question: If A is an n x n matrix, then A is called nilpotent if Ak = O for some positive integer k. (a) Prove that

If A is an n x n matrix, then A is called nilpotent if Ak = O for some positive integer k.
(a) Prove that every nilpotent matrix is singular.
(b) Verify that

is nilpotent.
(c) If A is nilpotent, prove that In - A is nonsingular.

A=1001

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