Answer
$$A^{-1}=\left[ \begin {array}{cccccc} 3.75&
0&- 1.25\\
3.45&- 1.0&- 1.37 \\
4.17& 0.0&- 2.5
\end {array} \right] .$$
Work Step by Step
To find $A^{-1}$, we have
$$\left[ A \ \ I \right]= \left[ \begin {array}{cccccc} 0.6&0&- 0.3&1&0&0\\
0.7&-1& 0.2&0&1&0\\ 1&0&- 0.9&0&0&1\end {array}
\right]
.
$$
Using Gauss-Jordan elimination, we get the row-reduced echelon form as follows
$$\left[I \ \ A^{-1} \right]=\left[ \begin {array}{cccccc} 1& 0& 0& 3.75&
0&- 1.25\\ 0& 1&0&
3.45&- 1.0&- 1.37 \\
0& 0& 1& 4.17& 0.0&- 2.5
\end {array} \right]
.
$$
Then $A^{-1}$ is given by
$$A^{-1}=\left[ \begin {array}{cccccc} 3.75&
0&- 1.25\\
3.45&- 1.0&- 1.37 \\
4.17& 0.0&- 2.5
\end {array} \right] .$$
