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).
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
Related questions
Question
answer it and explain correctly, thanks
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6df088ea-afc5-4002-86a7-62cf2caead1d%2F96a29e57-45d6-4321-883a-38772a14f34c%2Fbvxq9zv_processed.jpeg&w=3840&q=75)
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).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage