## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 8 - Section 8.4 - Multiplicative Inverses of Matrices and Matrix Equations - Exercise Set - Page 934: 89

#### Answer

The inverse is $\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]$.

#### Work Step by Step

Consider the given matrix $A=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]$. The inverse of matrix $A$ is equal to ${{A}^{-1}}=\frac{1}{ad-bc}\left[ \begin{matrix} d & -c \\ -d & a \\ \end{matrix} \right]$ Compare the matrix to the original matrix to get, \begin{align} & a=1 \\ & b=0 \\ & c=0 \\ & d=1 \end{align} The inverse is, ${{A}^{-1}}=\frac{1}{ad-bc}\left[ \begin{matrix} d & -c \\ -b & a \\ \end{matrix} \right]$ Substitute the values to get, \begin{align} & {{A}^{-1}}=\frac{1}{ad-bc}\left[ \begin{matrix} d & -c \\ -b & a \\ \end{matrix} \right] \\ & =\frac{1}{1}\left[ \begin{matrix} 1 & -0 \\ -0 & 1 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right] \end{align} Therefore, the inverse of the matrix $A$ is $\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]$

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