(1) True or False? Justify your answer. (a) Let A, B, and C be two square matrices of the same dimension and A be an invertible matrix then (A-¹BCA) 2023 A-¹B2023 C2023 A. True False Justification: = (b) Let A be an nxn matrix. The set of all n x n matrices X that satisfies (A²-31)X = O is not be closed under the matrix addition. True False Justification:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please justifiy using math

(1)
True or False? Justify your answer.
(a) Let A, B, and C be two square matrices of the same dimension and A be an invertible
matrix then (A-¹BCA) 2023 = A-1B2023 C2023 A.
True
False
Justification:
(b) Let A be an nxn matrix. The set of all nxn matrices X that satisfies (A²-31)X = O
is not be closed under the matrix addition.
True
False
Justification:
Transcribed Image Text:(1) True or False? Justify your answer. (a) Let A, B, and C be two square matrices of the same dimension and A be an invertible matrix then (A-¹BCA) 2023 = A-1B2023 C2023 A. True False Justification: (b) Let A be an nxn matrix. The set of all nxn matrices X that satisfies (A²-31)X = O is not be closed under the matrix addition. True False Justification:
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