Use Row Reduction to Find the Inverse of the Given $\left[ \begin{array} { c c c } 1 & 4 & - 1 \\4 & 5 & - 4 \\- 1 & 4 & 5\end{array} \right]$

Multiple Choice

Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication. $\left[ \begin{array} { c c c } 1 & 4 & - 1 \\4 & 5 & - 4 \\- 1 & 4 & 5\end{array} \right]$

A) $\left[ \begin{array} { c c c } - \frac { 41 } { 44 } & \frac { 6 } { 11 } & \frac { 1 } { 4 } \\\frac { 4 } { 11 } & - \frac { 1 } { 11 } & 0 \\- \frac { 21 } { 44 } & \frac { 2 } { 11 } & \frac { 1 } { 4 }\end{array} \right]$

B) $\left[ \begin{array} { c c c } - \frac { 25 } { 26 } & \frac { 4 } { 13 } & \frac { 19 } { 26 } \\\frac { 8 } { 13 } & - \frac { 1 } { 13 } & \frac { 4 } { 13 } \\- \frac { 1 } { 2 } & 0 & \frac { 1 } { 2 }\end{array} \right]$

C) $\left[ \begin{array} { c c c } - \frac { 41 } { 44 } & \frac { 4 } { 11 } & \frac { 21 } { 44 } \\\frac { 6 } { 11 } & - \frac { 1 } { 11 } & \frac { 2 } { 11 } \\- \frac { 1 } { 4 } & 0 & \frac { 1 } { 4 }\end{array} \right]$

D) $\left[ \begin{array} { c c c } - \frac { 25 } { 26 } & \frac { 8 } { 13 } & \frac { 1 } { 2 } \\\frac { 4 } { 13 } & - \frac { 1 } { 13 } & 0 \\- \frac { 19 } { 26 } & \frac { 4 } { 13 } & \frac { 1 } { 2 }\end{array} \right]$

E) The inverse matrix does not exist.