Use Row Reduction to Find the Inverse of the Given $\left[ \begin{array} { c c c c } 1 & 1 & - 1 & 1 \\- 3 & 1 & 1 & 0 \\- 3 & 1 & 0 & 1 \\8 & - 1 & - 1 & - 1\end{array} \right]$

Multiple Choice

Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication. $\left[ \begin{array} { c c c c } 1 & 1 & - 1 & 1 \\- 3 & 1 & 1 & 0 \\- 3 & 1 & 0 & 1 \\8 & - 1 & - 1 & - 1\end{array} \right]$

A) $\left[ \begin{array} { c c c c } 2 & - 1 & 5 & 5 \\3 & - 2 & 9 & - 1 \\- 4 & 3 & - 11 & - 10 \\1 & - 1 & 3 & 3\end{array} \right]$
B) $\left[ \begin{array} { c c c c } 2 & 3 & - 4 & 1 \\- 1 & - 2 & 3 & - 1 \\5 & 9 & - 11 & 3 \\5 & 8 & - 10 & 3\end{array} \right]$
C) $\left[ \begin{array} { c c c c } - 1 & 0 & 2 & 1 \\2 & 1 & - 3 & - 1 \\- 5 & 0 & 9 & 4 \\- 5 & - 1 & 10 & 4\end{array} \right]$
D) $\left[ \begin{array} { c c c c } - 1 & 2 & - 5 & - 5 \\0 & 1 & 0 & - 1 \\2 & - 3 & 9 & 10 \\1 & - 1 & 4 & 4\end{array} \right]$
E) The inverse matrix does not exist.