Show that if a square matrix A satisfies A2 − 4A + I = 0, then A is invertible and A−1 = 4I − A. Please show work.
Show that if a square matrix A satisfies A2 − 4A + I = 0, then A is invertible and A−1 = 4I − A. Please show work.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 72E: Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.
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Show that if a square matrix A satisfies A2 − 4A + I = 0, then A is invertible and A−1 = 4I − A.
Please show work.
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