College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 6 - Matrices and Determinants - Exercise Set 6.4 - Page 639: 4


$B$ is not the multiplicative inverse of $A$.

Work Step by Step

(See p.629) Let A be an $n\times$ n square matrix. If there is a square matrix $A^{-1}$ such that $AA^{-1}=I_{n}$ and $A^{-1}A=I_{n},$ then $A^{-1}$ is the multiplicative inverse of $A$. -------------- The products AB and BA should both be $I_{2}=\left[\begin{array}{ll} 1 & 0\\ 0 & 1 \end{array}\right].$ $AB=\left[\begin{array}{ll} -2(1)+4(-1) & -2(2)+4(-2)\\ 1(1)+(-2)(-1) & 1(2)+(-2)(-2) \end{array}\right]=\left[\begin{array}{ll} -6 & ...\\ ... & ... \end{array}\right]\neq I_{2}$ Since at least one of the products is NOT $I_{2}$, $B$ is not the multiplicative inverse of $A$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.