Answer
The provided matrix $ A=\left[ \begin{matrix}
3 & 2 \\
9 & 6 \\
\end{matrix} \right]$ is invertible; False.
Work Step by Step
Consider the matrix $ A=\left[ \begin{matrix}
3 & 2 \\
9 & 6 \\
\end{matrix} \right]$.
Now, we will check if the matrix is invertible or not.
Then, consider the matrix $ A=\left[ \begin{matrix}
3 & 2 \\
9 & 6 \\
\end{matrix} \right]$.
Now, the inverse of matrix $\left[ A \right]$ is equal to:
${{\left[ A \right]}^{-1}}=\frac{1}{\left| ad-bc \right|}\left[ \begin{matrix}
d & -b \\
-c & a \\
\end{matrix} \right]$
Now, compare the matrix to the original matrix.
So, $\begin{align}
& a=3 \\
& b=2 \\
& c=9 \\
& d=6
\end{align}$
Now, the inverse is:
${{\left[ A \right]}^{-1}}=\frac{1}{\left| ad-bc \right|}\left[ \begin{matrix}
d & -b \\
-c & a \\
\end{matrix} \right]$
Substitute the values to get, $\begin{align}
& {{\left[ A \right]}^{-1}}=\frac{1}{\left| ad-bc \right|}\left[ \begin{matrix}
d & -b \\
-c & a \\
\end{matrix} \right] \\
& =\frac{1}{\left| 18-18 \right|}\left[ \begin{matrix}
6 & -2 \\
-9 & 3 \\
\end{matrix} \right] \\
& =\frac{1}{0}\left[ \begin{matrix}
6 & -2 \\
-9 & 3 \\
\end{matrix} \right]
\end{align}$
So, $ ad-bc=0$ which shows that the matrix is not invertible.
