Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 10 - 10.3 - The Inverse of a Square Matrix - 10.3 Exercises - Page 734: 9

Answer

B is the inverse of A

Work Step by Step

When there is an inverse of a matrix $A A^{-1} = I$ (the Identity Matrix) $AB = \begin{bmatrix} 2 & -7 & 11 \\-1 & 11 & -7 \\ 0 &3 & -2 \end{bmatrix} \begin{bmatrix} 1 & 1 & 2 \\2 & 4 & -3 \\ 3 & 6 & -5 \end{bmatrix} =\begin{bmatrix} 1 & 0 &0\\ 0 & 1 &0 \\0 &0&1\end{bmatrix}$ and $BA = \begin{bmatrix} 1 & 1 & 2 \\2 & 4 & -3 \\ 3 & 6 & -5 \end{bmatrix} \begin{bmatrix} 2 & -7 & 11 \\-1 & 11 & -7 \\ 0 &3 & -2 \end{bmatrix}=\begin{bmatrix} 1 & 0 &0\\ 0 & 1 &0 \\0 &0&1\end{bmatrix}$ Since $AB=BA$ equals the identity matrix, B is the inverse of A.
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