Use the Gauss-Jordan method to compute the inverse, if it exists, of the matrix.
$\begin{bmatrix} 1 & 2 & 0 \\ 1 & -2 & 1 \\ 0 & 3 & -1 \end{bmatrix}$
Find the inverse. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $M^{-1} = \boxed{}$ (Simplify your answer.)
B. Finding the inverse is not possible.