Answer
See below.
Work Step by Step
We know that for a matrix
\[
\left[\begin{array}{rr}
a & b \\
c &d \\
\end{array} \right]
\]
the determinant, $D=ad-bc.$
Hence here $D=5\cdot3-4\cdot2=15-8=7.$
Thus the value of the second-order (because it is a $2$ by $2$ matrix) determinant
is $7$.
