## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 10 - 10.3 - The Inverse of a Square Matrix - 10.3 Exercises - Page 734: 15

#### Answer

$\begin{bmatrix} -3 &2 \\ -2 & 1\end{bmatrix}$

#### Work Step by Step

$A=\begin{bmatrix} 1 & -2 \\ 2 & -3\end{bmatrix}$ Therefore, the general form of a matrix of order $2 \times 2$ is: $\begin{bmatrix} p & q \\ r & s\end{bmatrix}=ps-qr$ Now, $ps-qr=\begin{bmatrix} 1 & -2 \\ 2 & -3\end{bmatrix}=-3+4=1 \ne 0$ $A^{-1}=\dfrac{1}{1} \begin{bmatrix} -3 & 2 \\ -2 & -1 \end{bmatrix}$ Our answer is: $\begin{bmatrix} -3 &2 \\ -2 & 1\end{bmatrix}$

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