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2- An n xn-matrix P is called an idempotent if P2 = P. A matrix is called self-inverse if A-¹ = A. Show the following statements. a) b) In is the only invertible idempotent. U is self-inverse if and only if U = I - 2P for some idempotent P.

2- An n xn-matrix P is called an idempotent if P2 = P. A matrix is called self-inverse if A-¹ = A. Show the following statements. a) b) In is the only invertible idempotent. U is self-inverse if and only if U = I - 2P for some idempotent P.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.3: The Inverse Of A Matrix
Problem 44EQ
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2- An n x n-matrix P is called an idempotent if P2 = P. A matrix is called self-inverse if A-¹ = A. Show the following statements. a) b) In is the only invertible idempotent. U is self-inverse if and only if U = I -2P for some idempotent P.
Transcribed Image Text:2- An n x n-matrix P is called an idempotent if P2 = P. A matrix is called self-inverse if A-¹ = A. Show the following statements. a) b) In is the only invertible idempotent. U is self-inverse if and only if U = I -2P for some idempotent P.
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