5. (8 points) Let A € M₂ (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(A-¹).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 13E
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5. (8 points) Let A € M₂ (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(A-¹).
Transcribed Image Text:5. (8 points) Let A € M₂ (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(A-¹).
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