Answer
$1$
Work Step by Step
Expansion across first row:
$\begin{align}
\det A & = 0\begin{vmatrix}-3&0\\3&1\end{vmatrix}-4\begin{vmatrix}5&0\\2&1\end{vmatrix}+1\begin{vmatrix}5&-3\\2&3\end{vmatrix}\\
& = 0(-3-0)-4(5-0)+1(15+6)\\
& = 0-20+21=1
\end{align}$
Expansion down second column:
$\begin{align}
\det A & = -4\begin{vmatrix}5&0\\2&1\end{vmatrix}-3\begin{vmatrix}0&1\\2&1\end{vmatrix}-3\begin{vmatrix}0&1\\5&0\end{vmatrix}\\
& = -4(5-0)+-3(0-2)-3(0-5)\\
& = -20+6+15=1
\end{align}$
