1. Recall that if A and B are invertible matrices, (AB)-¹ = B-¹A¯¹. (a) Give a counterexample to show that (AB)-¹ # A-¹B-¹ in general (b) Find conditions which will guarantee that (AB)-¹ = A¯¹B-¹

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 34E
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1. Recall that if A and B are invertible matrices, (AB)-¹ = B-¹A-¹.
(a) Give a counterexample to show that (AB)-¹ # A-¹B-¹ in general.
(b) Find conditions which will guarantee that (AB)-¹ = A-¹B-¹
Transcribed Image Text:1. Recall that if A and B are invertible matrices, (AB)-¹ = B-¹A-¹. (a) Give a counterexample to show that (AB)-¹ # A-¹B-¹ in general. (b) Find conditions which will guarantee that (AB)-¹ = A-¹B-¹
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