Use Row Reduction to Find the Inverse of the Given $\left[ \begin{array} { c c c c } 1 & 1 & - 1 & 1 \\- 2 & 1 & 1 & 0 \\- 2 & 1 & 0 & 1 \\4 & - 1 & - 1 & - 1\end{array} \right]$

Multiple Choice

Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication. $\left[ \begin{array} { c c c c } 1 & 1 & - 1 & 1 \\- 2 & 1 & 1 & 0 \\- 2 & 1 & 0 & 1 \\4 & - 1 & - 1 & - 1\end{array} \right]$

A) $\left[ \begin{array} { c c c c } - 3 & - 4 & 6 & - 1 \\4 & 5 & - 7 & 1 \\5 & 8 & - 11 & 2 \\5 & 7 & - 10 & 2\end{array} \right]$
B) $\left[ \begin{array} { c c c c } - 3 & 4 & 5 & 5 \\- 4 & 5 & 8 & - 1 \\6 & - 7 & - 11 & - 10 \\- 1 & 1 & 2 & 2\end{array} \right]$
C) $\left[ \begin{array} { c c c c } 1 & 0 & - 2 & - 1 \\0 & 1 & 1 & 1 \\2 & 0 & - 5 & - 3 \\2 & - 1 & - 4 & - 3\end{array} \right]$
D) $\left[ \begin{array} { c c c c } 1 & 0 & 2 & 2 \\0 & 1 & 0 & - 1 \\- 2 & 1 & - 5 & - 4 \\- 1 & 1 & - 3 & - 3\end{array} \right]$
E) The inverse matrix does not exist.