Using elementary row transformations find the inverse of the matrix `[{:(3,0,-1),(2,3,0),(0,4,1):}]`

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{pmatrix} \) using elementary row transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations to convert \( A \) into \( I \). The augmented matrix will look like this:

\[
\left( \begin{array}{ccc|ccc}
3 & 0 & -1 & 1 & 0 & 0 \\
2 & 3 & 0 & 0 & 1 & 0 \\
0 & 4 & 1 & 0 & 0 & 1
\end{array} \right)
...