Answer
$30$
Work Step by Step
Expansion across first row:
$\begin{align}
\det A & = 1\begin{vmatrix}1&1\\4&2\end{vmatrix}-2\begin{vmatrix}3&1\\2&2\end{vmatrix}+4\begin{vmatrix}3&1\\2&4\end{vmatrix}\\
& = 1(2-4)-2(6-2)+4(12-2)\\
& = -2-8+40=30
\end{align}$
Expansion down second column:
$\begin{align}
\det A & = -2\begin{vmatrix}3&1\\2&2\end{vmatrix}+1\begin{vmatrix}1&4\\2&2\end{vmatrix}-4\begin{vmatrix}1&4\\3&1\end{vmatrix}\\
& = -2(6-2)+1(2-8)-4(1-12)\\
& = -8-6+44=30
\end{align}$
