Question: Let A and B be n n idempotent matrices. (See Exercise 19.) (a) Show that AB is idempotent if AB = BA. (b) Show

Let A and B be n × n idempotent matrices. (See Exercise 19.)
(a) Show that AB is idempotent if AB = BA.
(b) Show that if A is idempotent, then AT is idempotent.
(c) Is A + B idempotent? Justify your answer.
(d) Find all values of k for which k A is also idempotent.

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