Question: If A is an n n matrix, then A is called idempotent if A2 = A. (a) Verify that In and O are idempotent.

If A is an n × n matrix, then A is called idempotent if A2 = A.
(a) Verify that In and O are idempotent.
(b) Find an idempotent matrix that is not In or O.
(c) Prove that the only n × n nonsingular idempotent matrix is In.

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