Answer
$0$
Work Step by Step
Expansion across first row:
$\begin{align}
\det A & = 2\begin{vmatrix}1&2\\3&-1\end{vmatrix}+2\begin{vmatrix}3&2\\1&-1\end{vmatrix}+3\begin{vmatrix}3&1\\1&3\end{vmatrix}\\
& = 2(-1-6)+2(-3-2)+3(9-1)\\
& = -14-10+24=0
\end{align}$
Expansion down second column:
$\begin{align}
\det A & = 2\begin{vmatrix}3&2\\1&-1\end{vmatrix}+1\begin{vmatrix}2&3\\1&-1\end{vmatrix}-3\begin{vmatrix}2&3\\3&2\end{vmatrix}\\
& = 2(-3-2)+1(-2-3)-3(4-9)\\
& = -10-5+15=0
\end{align}$
