Answer
$A^{-1}=\left[\begin{array}{llll}
0 & -1 & 0 & 1\\
-1 & -5 & 0 & 3\\
-2 & -4 & 1 & -2\\
-1 & -4 & 0 & 1
\end{array}\right]$
Work Step by Step
Technology used: the free online calculator at
www.geogebra.org/classic/cas
The syntax for defining a matrix:
A:= { { row 1}, {row 2} ... { row n} },
(the elements in rows are delimited with commas)
(A "colon equals" assigns the matrix to A).
The command for $B=A^{-1}$ is B:= Invert ( A ).
(B "colon equals" assigns the matrix to B).
Check by multiplying the matrices
AB=BA=I
Please see screenshot below.
$A^{-1}=\left[\begin{array}{llll}
0 & -1 & 0 & 1\\
-1 & -5 & 0 & 3\\
-2 & -4 & 1 & -2\\
-1 & -4 & 0 & 1
\end{array}\right]$