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

Multiple Choice

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

A)
$$\left[ \begin{array} { c c c c } \frac { 1 } { 2 } & - \frac { 1 } { 3 } & 0 & \frac { 1 } { 2 } \\\frac { 1 } { 6 } & - \frac { 1 } { 6 } & 0 & \frac { 1 } { 4 } \\\frac { 1 } { 6 } & - \frac { 1 } { 12 } & 0 & \frac { 1 } { 6 } \\0 & 0 & - \frac { 1 } { 6 } & 0\end{array} \right]$$

B) The inverse does not exist.

C)
$\left[\begin{array}{rrrr}-1 & \frac{1}{2} & 0 & 0 \\1 & 0 & -\frac{1}{3} & 0 \\0 & 0 & 0 & -\frac{1}{6} \\3&-\frac{1}{2} & -\frac{1}{2} & 0\end{array}\right]$

D)
$\left[\begin{array}{rrrr}-1 & 1 & 0 & 3 \\\frac{1}{2} & 0 & 0 & -\frac{1}{2} \\0 & -\frac{1}{3} & 0 & -\frac{1}{2} \\0 & 0 & -\frac{1}{6} & 0\end{array}\right]$