Use Row Reduction to Find the Inverse of the Given $\left[ \begin{array} { c c c } 1 & 9 & 10 \\0 & 9 & 10 \\1 & 0 & 1\end{array} \right]$

Use row reduction to find the inverse of the given matrix, if it exists. Check your answer by multiplication.
$\left[ \begin{array} { c c c } 1 & 9 & 10 \\0 & 9 & 10 \\1 & 0 & 1\end{array} \right]$

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