Find the Inverse, If It Exists, for the Matrix $$A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$$

Find the inverse, if it exists, for the matrix.
- $$A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$$

A)
$$\left[\begin{array}{cccc}\frac{1}{2} & -\frac{1}{3} & 0 & \frac{1}{2} \\\frac{1}{6} & -\frac{1}{6} & 0 & \frac{1}{4} \\\frac{1}{6} & -\frac{1}{12} & 0 & \frac{1}{6} \\0 & 0 & -\frac{1}{2} & 0\end{array}\right]B) \left[\begin{array}{cccc}-1 & 1 & 0 & 3 \\\frac{1}{2} & 0 & 0 & -\frac{1}{2} \\0 & -\frac{1}{3} & 0 & -\frac{1}{2} \\0 & 0 & -\frac{1}{2} & 0\end{array}\right]$$
C) $$\left[\begin{array}{cccc}-1 & \frac{1}{2} & 0 & 0 \\1 & 0 & -\frac{1}{3} & 0 \\0 & 0 & 0 & -\frac{1}{2} \\3-\frac{1}{2} & -\frac{1}{2} & 0\end{array}\right]$$
D) No inverse