Answer
The determinant is $-42$.
Work Step by Step
In order to calculate the given determinant, first evaluate the individual determinant separately. So consider,
$\begin{align}
& \left| \begin{matrix}
3 & 1 \\
-2 & 3 \\
\end{matrix} \right|=3\left( 3 \right)-\left( -2 \right)1 \\
& =9+2 \\
& =11
\end{align}$
Next consider,
$\begin{align}
& \left| \begin{matrix}
7 & 0 \\
1 & 5 \\
\end{matrix} \right|=7\left( 5 \right)-1\left( 0 \right) \\
& =35-0 \\
& =35
\end{align}$
Now find,
$\begin{align}
& \left| \begin{matrix}
3 & 0 \\
0 & 7 \\
\end{matrix} \right|=3\left( 7 \right)-0 \\
& =21-0 \\
& =21
\end{align}$
And finally find,
$\begin{align}
& \left| \begin{matrix}
9 & -6 \\
3 & 5 \\
\end{matrix} \right|=9\left( 5 \right)-3\left( -6 \right) \\
& =45+18 \\
& =63
\end{align}$
Hence,
$\left| \begin{matrix}
\left| \begin{matrix}
3 & 1 \\
-2 & 3 \\
\end{matrix} \right| & \left| \begin{matrix}
7 & 0 \\
1 & 5 \\
\end{matrix} \right| \\
\left| \begin{matrix}
3 & 0 \\
0 & 7 \\
\end{matrix} \right| & \left| \begin{matrix}
9 & -6 \\
3 & 5 \\
\end{matrix} \right| \\
\end{matrix} \right|=\left| \begin{matrix}
11 & 35 \\
21 & 63 \\
\end{matrix} \right|$
Now calculate,
$\begin{align}
& \left| \begin{matrix}
11 & 35 \\
21 & 63 \\
\end{matrix} \right|=11\left( 63 \right)-21\left( 35 \right) \\
& =693-735 \\
& =-42
\end{align}$
