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44. A square matrix A is called idempotent if A² = A. (The word idempotent comes from the Latin idem, meaning "same," and potere, meaning "to have power." Thus, something that is idempotent has the "same power" when squared.) a. Find three idempotent 2 × 2 matrices. b. Prove that the only invertible idempotent n x n matrix is the identity matrix.

44. A square matrix A is called idempotent if A² = A. (The word idempotent comes from the Latin idem, meaning "same," and potere, meaning "to have power." Thus, something that is idempotent has the "same power" when squared.) a. Find three idempotent 2 × 2 matrices. b. Prove that the only invertible idempotent n x n matrix is the identity matrix.

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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please answer both parts A and B

44. A square matrix A is called idempotent if A² A. (The word idempotent comes from the Latin idem, meaning "same," and potere, meaning "to have power." Thus, something that is idempotent has the "same power" when squared.) = a. Find three idempotent 2 × 2 matrices. b. Prove that the only invertible idempotent n - n matrix is the identity matrix.
Transcribed Image Text:44. A square matrix A is called idempotent if A² A. (The word idempotent comes from the Latin idem, meaning "same," and potere, meaning "to have power." Thus, something that is idempotent has the "same power" when squared.) = a. Find three idempotent 2 × 2 matrices. b. Prove that the only invertible idempotent n - n matrix is the identity matrix.
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