# Chapter 8 - Section 8.4 - Multiplicative Inverses of Matrices and Matrix Equations - Exercise Set - Page 932: 18

The matrix does not have an inverse.

#### Work Step by Step

Consider the given matrix $A=\left[ \begin{matrix} 6 & -3 \\ -2 & 1 \\ \end{matrix} \right]$ Now, by using the inverse formula we get: ${{A}^{-1}}=\frac{1}{\left| ad-bc \right|}\left[ \begin{matrix} d & -b \\ -c & a \\ \end{matrix} \right]$ Let, \begin{align} & a=6 \\ & b=-3 \\ & c=-2 \\ & d=1 \end{align} Substitute the values to get \begin{align} & {{A}^{-1}}=\frac{1}{\left| ad-bc \right|}\left[ \begin{matrix} d & -b \\ -c & a \\ \end{matrix} \right] \\ & {{A}^{-1}}=\frac{1}{\left| 6\times 1-\left( -3 \right)\times \left( -2 \right) \right|}\left[ \begin{matrix} 1 & 3 \\ 2 & 6 \\ \end{matrix} \right] \\ & =\frac{1}{0}\left[ \begin{matrix} 2 & -3 \\ 1 & 2 \\ \end{matrix} \right] \end{align} So, therefore the matrix does not have an inverse $ab-bc=0$

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