Answer
$A^{-1}=\left[\begin{array}{llll}
3/5 & 0 & -2/5 & 1/5\\
1/5 & 0 & 1/5 & -1/10\\
0 & 1 & 0 & 0\\
-6/5 & 0 & 4/5 & 1/10
\end{array}\right]$
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.
$A^{-1}=\left[\begin{array}{llll}
3/5 & 0 & -2/5 & 1/5\\
1/5 & 0 & 1/5 & -1/10\\
0 & 1 & 0 & 0\\
-6/5 & 0 & 4/5 & 1/10
\end{array}\right]$
