#### Answer

If $ A=\left[ \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right]$, the matrix $ A $ is invertible if and only if $ ad-bc\ne 0$.

#### Work Step by Step

Consider the matrix $ A=\left[ \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right]$.
Now, we will check if the matrix is invertible or not.
The inverse of matrix $\left[ A \right]$ is equal to:
${{\left[ A \right]}^{-1}}=\frac{1}{ad-bc}\left[ \begin{matrix}
d & -b \\
-c & a \\
\end{matrix} \right]$
Thus, $ ad-bc\ne 0$ for the matrix to be invertible.