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E3.3. (20) Suppose that A and B are n×n matrices. a. Show that if A is invertible, then so is 3A. In the case when A is invertible, find the inverse of 3A in terms of A¹. b. Show that if AB is invertible, then so is A. (Hint for part b.: There is a matrix R such that (AB)R=I. Why?)

E3.3. (20) Suppose that A and B are n×n matrices. a. Show that if A is invertible, then so is 3A. In the case when A is invertible, find the inverse of 3A in terms of A¹. b. Show that if AB is invertible, then so is A. (Hint for part b.: There is a matrix R such that (AB)R=I. Why?)

Advanced Engineering Mathematics
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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E3.3. (20) Suppose that A and B are n×n matrices. a. Show that if A is invertible, then so is 3A. In the case when A is invertible, find the inverse of 3A in terms of A¹. b. Show that if AB is invertible, then so is A. (Hint for part b.: There is a matrix R such that (AB) R=1. Why?)
Transcribed Image Text:E3.3. (20) Suppose that A and B are n×n matrices. a. Show that if A is invertible, then so is 3A. In the case when A is invertible, find the inverse of 3A in terms of A¹. b. Show that if AB is invertible, then so is A. (Hint for part b.: There is a matrix R such that (AB) R=1. Why?)
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