Answer
$\left| \begin{matrix}
5 & 4 \\
2 & 3 \\
\end{matrix} \right|=\underset{\scriptscriptstyle-}{5}\cdot \underset{\scriptscriptstyle-}{3}-\underset{\scriptscriptstyle-}{4}\cdot \underset{\scriptscriptstyle-}{2}=\underline{15}-\underset{\scriptscriptstyle-}{8}=\underset{\scriptscriptstyle-}{7}$
The value of this second-order determinant is 7.
Work Step by Step
$\text{For any determinant,}$
$\left| \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right|=ad-bc$
$\text{then for the given determinant}$
$\begin{align}
& \left| \begin{matrix}
5 & 4 \\
2 & 3 \\
\end{matrix} \right|=5\cdot 3-4\cdot 2 \\
& =15-8 \\
& =7
\end{align}$
