Find the Inverse, If It Exists, of the Given Matrix $\left[\begin{array}{rrr}-2 & 1 & 3 \\ 3 & -1 & 2 \\ -4 & 2 & 0\end{array}\right]$

Multiple Choice

Find the inverse, if it exists, of the given matrix.
- $\left[\begin{array}{rrr}-2 & 1 & 3 \\ 3 & -1 & 2 \\ -4 & 2 & 0\end{array}\right]$

A) $$\left[\begin{array}{ccc}-\frac{2}{3} & 1 & \frac{5}{6} \\-1 & 2 & 2 \\\frac{1}{3} & 0 & -\frac{1}{6}\end{array}\right]$$
B) $$\left[\begin{array}{ccc}-1 & 1 & \frac{5}{6} \\-\frac{4}{3} & 2 & \frac{13}{6} \\\frac{1}{3} & 0 & -\frac{1}{6}\end{array}\right]$$
C) $\left[\begin{array}{ccc}-\frac{2}{3} & 1 & \frac{5}{6} \\ -\frac{4}{3} & 2 & \frac{13}{6} \\ \frac{1}{3} & 0 & 0\end{array}\right]$
D) $$\left[\begin{array}{ccc}-\frac{2}{3} & 1 & \frac{5}{6} \\-\frac{4}{3} & 2 & \frac{13}{6} \\\frac{1}{3} & 0 & -\frac{1}{6}\end{array}\right]$$