Answer
The second and third columns of $A^{-1}$ is
$\begin{bmatrix}
1.5&-4.5\\
-433/6&219.5\\
68/3&-69
\end{bmatrix}$
Work Step by Step
Let us write the matrix $[A\ e_2\ e_3]$
$\begin{bmatrix}
-25&-9&-27&0&0\\
546&180&537&1&0\\
154&50&149&0&1
\end{bmatrix}$
If we row reduce this such that the first three columns form the identity matrix, the fourth and fifth columns will be the second and third columns of the inverse of A.
$\begin{bmatrix}
1&0&0&1.5&-4.5\\
0&1&0&-433/6&219.5\\
0&0&1&68/3&-69
\end{bmatrix}$
