Find the Inverse, If It Exists, for the Matrix $\left[ \begin{array} { l l l } 1 & 1 & 1 \\ 2 & 1 & 1 \\ 2 & 2 & 3 \end{array} \right]$

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $\left[ \begin{array} { l l l } 1 & 1 & 1 \\ 2 & 1 & 1 \\ 2 & 2 & 3 \end{array} \right]$

A) The inverse does not exist.
B) $$\left[ \begin{array} { r r r } - 1 & 1 & 0 \\4 & - 1 & - 1 \\- 2 & 0 & 1\end{array} \right]$$
C)
$$\left[ \begin{array} { l l l } - 1 & - 1 & - 1 \\- 2 & - 1 & - 1 \\- 2 & - 2 & - 3\end{array} \right]$$

D)

$$\left[ \begin{array} { c c c } 1 & 1 & 1 \\\frac { 1 } { 2 } & 1 & 1 \\\frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 }\end{array} \right]$$