i) Let A, B&Man (IR) So that AB = In is so BA=In too. happened.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.3: The Inverse Of A Matrix
Problem 44EQ
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3 fees & fe
Prove the following daims:
i) Let A, B.-€ Mnxn (IR) so that AB = In is happened.
So BA=In too.
ii) Let A & M Kn(R) and BeMaxk (TR) forkyn.
Then AB # Ik
kan
iii) Let A, B be square matrixes. Prove that if AB
is invertible thenA is invertible too.
Transcribed Image Text:3 fees & fe Prove the following daims: i) Let A, B.-€ Mnxn (IR) so that AB = In is happened. So BA=In too. ii) Let A & M Kn(R) and BeMaxk (TR) forkyn. Then AB # Ik kan iii) Let A, B be square matrixes. Prove that if AB is invertible thenA is invertible too.
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