An n × 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

Transcribed Image Text:

I- aPy = 1+) P.