Determine the Inverse of the Given Matrix, If Possible $A=\left[\begin{array}{rrrr}-5 & 5 & 3 & -4 \\0 & 1 & -2 & 0 \\3 & 2 & 1 & 3 \\0 & 1 & 1 & 0\end{array}\right]$

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
- $A=\left[\begin{array}{rrrr}-5 & 5 & 3 & -4 \\0 & 1 & -2 & 0 \\3 & 2 & 1 & 3 \\0 & 1 & 1 & 0\end{array}\right]$

A) $A^{-1}=\left[\begin{array}{rrrr}-1 & -\frac{10}{9} & -\frac{4}{3} & -\frac{59}{9} \\0 & -\frac{1}{3} & 0 & -\frac{2}{3} \\0 & \frac{1}{3} & 0 & -\frac{1}{3} \\1 & \frac{11}{9} & \frac{5}{3} & \frac{64}{9}\end{array}\right]$

B) $A^{-1}=\left[\begin{array}{rrrr}-1 & \frac{10}{9} & -\frac{4}{3} & \frac{59}{9} \\0 & \frac{1}{3} & 0 & \frac{2}{3} \\0 & -\frac{1}{3} & 0 & \frac{1}{3} \\1 & -\frac{11}{9} & \frac{5}{3} & -\frac{64}{9}\end{array}\right]$

C) $\text { Singular matrix }$

D) $A^{-1}=\left[\begin{array}{cccc}1 & \frac{10}{9} & \frac{4}{3} & \frac{59}{9} \\0 & \frac{1}{3} & 0 & \frac{2}{3} \\0 & -\frac{1}{3} & 0 & \frac{1}{3} \\-1 & -\frac{11}{9} & -\frac{5}{3} & -\frac{64}{9}\end{array}\right]$