Find the inverse of the given matrix, if it exists. Use the algorithm for finding \( A^{-1} \) by row reducing [A I]. \[ A=\left[\begin{array}{rrr} 1 & 0 & 4 \\ -2 & 1 & -4 \\ 2 & 3 & -4 \end{array}\r Set up the matrix [A I].[AI]=(Type an integer or simplified fraction for each matrix element.)
