# Chapter 8 - Section 8.4 - Multiplicative Inverses of Matrices and Matrix Equations - Exercise Set - Page 934: 68

The inverse is $A=\left[ \begin{matrix} 1 & 1 & 1 \\ 3 & 5 & 4 \\ 3 & 6 & 5 \\ \end{matrix} \right]$.

#### Work Step by Step

Consider the given matrix, $A=\left[ \begin{matrix} 1 & 1 & -1 \\ -3 & 2 & -1 \\ 3 & -3 & 2 \\ \end{matrix} \right]$ We have to find the inverse of matrix $A$ by using a calculator. We will follow the steps given below: (1) We select the matrix $A$ from the matrix edit menu and then enter or accept the dimensions. (2) Use ${{2}^{nd}}$ and press the matrix button. (3) Select the matrix $A$ and use the function ${{X}^{-1}}$ for the inverse of matrix $A$ and press enter. (4) We find the ${{A}^{-1}}$ Therefore, the inverse of the matrix $A$ is $\left[ \begin{matrix} 1 & 1 & 1 \\ 3 & 5 & 4 \\ 3 & 6 & 5 \\ \end{matrix} \right]$. Now, check the result: show that $A{{A}^{-1}}=I$. When we multiply matrix $A$ with ${{A}^{-1}}$ we obtain the identity matrix, so the given matrix is correct.

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