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For these two problems, use the definition of eigenvalues. (a) An n × n matrix is...

For these two problems, use the definition of eigenvalues.

(a) An n × n matrix is said to be nilpotent if Ak = O for some positive integer k. Show that all eigenvalues of a nilpotent matrix are 0.

(b) An n × n matrix is said to be idempotent if A2 = A. Show that all eigenvalues of a idempotent matrix are 0, or 1.

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