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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please answer both parts A and B
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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