Answer
If $A=\left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right]$, then
$A^{-1}=\displaystyle \frac{1}{ad-bc}\left[\begin{array}{ll}
d & -b\\
-c & a
\end{array}\right]$.
Work Step by Step
Let $A=\left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right]$.
The matrix $A$ is invertible if and only if $ad-bc\neq 0$.
If $ad-bc=0$, then $A $ does not have a multiplicative inverse.
If $A=\left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right]$, then
$A^{-1}=\displaystyle \frac{1}{ad-bc}\left[\begin{array}{ll}
d & -b\\
-c & a
\end{array}\right]$.
