Using elementary transformations, find the inverse of the matrix`[[2, 0,-1],[ 5, 1, 0],[ 0, 1 ,3]]`

Explanation

To find the inverse of the matrix \( A = \begin{bmatrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{bmatrix} \) using elementary transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations to transform \( A \) into \( I \). The augmented matrix will look like this:

\[
\begin{bmatrix}
2 & 0 & -1 & | & 1 & 0 & 0 \\
5 & 1 & 0 & | & 0 & 1 & 0 \\
0 & 1 & 3 & | & 0 & 0 & 1
\end{bmatrix}
...