Question: An n Ã n matrix P is called an idempotent if P2 = P. Show that: (a) I is the only invertible idempotent. (b) P

An n Ã— n matrix P is called an idempotent if P2 = P. Show that:
(a) I is the only invertible idempotent.
(b) P is an idempotent if and only if I - 2P is self-inverse.
(c) U is self-inverse if and only if U = I - 2P for some idempotent P.
(d) I - aP is invertible for any a ‰ 1, and

I- aPy = 1+) P.

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