Answer
See the proof below.
Work Step by Step
Since $A$ is invertible, then it has the inverse matrix $A^{-1}$.
Thus $AB=O$ implies $A^{-1}(AB)=A^{-1}O=O$ and then
$(A^{-1}A)B=IB=B=O$
Therefore, $B=O$
Elementary Linear Algebra 7th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
1-13311-087-8
ISBN 13:
978-1-13311-087-3
Chapter 2 - Matrices - 2.3 The Inverse of a Matrix - 2.3 Exercises - Page 73: 71
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