Answer
\[
M=
\left[ {\begin{array}{cc}
-2/25 & 3/25 & -1/25\\
2/5 & 2/5 & 1/5 \\
-1/5 & -1/5 & -3/5 \\
\end{array} } \right]
\]
Work Step by Step
We plug this into a graphing calculator as stated in the book. It is important to remember the calculator will find the inverse by solving for a second matrix, and thus the answer will be a decimal on most calculator. If using a TI calculator, pushing $\triangle frac$ will put the answer into fractions.
After doing above we get...
\[
M=
\left[ {\begin{array}{cc}
-2/25 & 3/25 & -1/25\\
2/5 & 2/5 & 1/5 \\
-1/5 & -1/5 & -3/5 \\
\end{array} } \right]
\]