. Let A and B be square n x n matrices. Show that det AB = det BA even though in general, AB ‡ BA. • Prove that if A is invertible, then det (A-¹) = (det A)-¹. .
. Let A and B be square n x n matrices. Show that det AB = det BA even though in general, AB ‡ BA. • Prove that if A is invertible, then det (A-¹) = (det A)-¹. .
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.5: Determinants
Problem 82E: Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.
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![. Let A and B be square n x n matrices. Show that det AB
det BA even though in general, AB ‡ BA.
• Prove that if A is invertible, then det (A-¹) = (det A)-¹.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30f79184-3047-455a-b3d8-f2ad47623cdf%2Fae1a12e8-d6c6-4d7e-aefa-7e5bf5efd383%2Fotamgj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:. Let A and B be square n x n matrices. Show that det AB
det BA even though in general, AB ‡ BA.
• Prove that if A is invertible, then det (A-¹) = (det A)-¹.
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