5. Let A E M, (R) be given. (a) If det(A) = 1, prove that adj (adj(A)) = A. (b) If A is nonsingular, prove that adj(A) is nonsingular and adj(A)-¹ = adj (1-¹).
5. Let A E M, (R) be given. (a) If det(A) = 1, prove that adj (adj(A)) = A. (b) If A is nonsingular, prove that adj(A) is nonsingular and adj(A)-¹ = adj (1-¹).
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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Help me answer question 5
Transcribed Image Text:5.
Let A € M₂ (R) be given.
(a) If det(A) = 1, prove that adj (adj (4)) = A.
(b) If A is nonsingular, prove that adj(A) is nonsingular and adj(A)-¹ = adj(A-¹).
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