Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 2 - Matrices - 2.1 Operations with Matrices - 2.1 Exercises - Page 49: 57

Answer

$$AA=\left[\begin{array}{rrr}{1} & {0} & {0} \\ {0} & {4} & {0} \\ {0} & {0} & {9}\end{array}\right] .$$

Work Step by Step

Given $$ A=\left[\begin{array}{rrr}{-1} & {0} & {0} \\ {0} & {2} & {0} \\ {0} & {0} & {3}\end{array}\right]. $$ We have \begin{align*} AA&= \left[\begin{array}{rrr}{-1} & {0} & {0} \\ {0} & {2} & {0} \\ {0} & {0} & {3}\end{array}\right]\left[\begin{array}{rrr}{-1} & {0} & {0} \\ {0} & {2} & {0} \\ {0} & {0} & {3}\end{array}\right]\\ &=\left[\begin{array}{rrr}{1} & {0} & {0} \\ {0} & {4} & {0} \\ {0} & {0} & {9}\end{array}\right] . \end{align*}
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