Use the Row Reduction Method to Find the Inverse of the Matrix

Multiple Choice

Use the row reduction method to find the inverse of the matrix, if it exists. $A = \left[ \begin{array} { c c c } 1 & 3 & 0 \\- 1 & 3 & 0 \\3 & 0 & 2\end{array} \right]$

A) $\left[ \begin{array} { c c c } \frac { 1 } { 6 } & \frac { 1 } { 6 } & 0 \\- \frac { 3 } { 4 } & \frac { 3 } { 4 } & \frac { 1 } { 2 } \\\frac { 1 } { 2 } & - \frac { 1 } { 2 } & 0\end{array} \right]$
B) $\left[ \begin{array} { c c c } \frac { 1 } { 2 } & - \frac { 1 } { 2 } & 0 \\\frac { 1 } { 6 } & \frac { 1 } { 6 } & 0 \\- \frac { 3 } { 4 } & \frac { 3 } { 4 } & \frac { 1 } { 2 }\end{array} \right]$
C) $\left[ \begin{array} { c c c } \frac { 1 } { 2 } & - \frac { 1 } { 2 } & 0 \\\frac { 1 } { 6 } & \frac { 1 } { 6 } & 0 \\\frac { 3 } { 4 } & - \frac { 3 } { 4 } & \frac { 1 } { 2 }\end{array} \right]$
D) $\left[ \begin{array} { c c c } \frac { 1 } { 6 } & \frac { 1 } { 6 } & 0 \\\frac { 1 } { 2 } & - \frac { 1 } { 2 } & 0 \\- \frac { 3 } { 4 } & \frac { 3 } { 4 } & \frac { 1 } { 2 }\end{array} \right]$
E) The inverse matrix does not exist.