Answer
The given matrix has a determinant of zero therefore it has no inverse.
(Refer to the step-by-step for the solution.)
Work Step by Step
We know that for a matrix
\[
\left[\begin{array}{rr}
a & b \\
c &d \\
\end{array} \right]
\]
the determinant $D$ can be computed using the formula
$D=ad-bc$
We also know that if the determinant is $0$ $(D=0)$, then the matrix has no inverse.
Note that the given matrix has
$D=(4\cdot1)-(2\cdot2)\\
D=4-4\\
D=0$
The determinant is zero therefore the given matrix has no inverse.
