$$A= \left[\begin{matrix} 3 & -1 & 2 \\-2 & 1 & 2 \\3 & -1 & 4 \end{matrix}\right]$$
$A≔\left(\begin{matrix}3&-1&2\\-2&1&2\\3&-1&4\end{matrix}\right)$
$\left[\begin{array}{rrr}6 & 2 & -4 \\ 14 & 6 & -10 \\ -1 & 0 & 1\end{array}\right]$
$A_{11}=\left|\begin{array}{rr}1 & 2 \\ -1 & 4\end{array}\right|=6$
$A_{12}=-\left|\begin{array}{rr}-2 & 2 \\ 3 & 4\end{array}\right|=14$
$A_{13}=\left|\begin{array}{rr}-2 & 1 \\ 3 & -1\end{array}\right|=-1$
$A_{21}=-\left|\begin{array}{rr}-1 & 2 \\ -1 & 4\end{array}\right|=2$
$A_{22}=\left|\begin{array}{rr}3 & 2 \\ 3 & 4\end{array}\right|=6$
$A_{23}=-\left|\begin{array}{rr}3 & -1 \\ 3 & -1\end{array}\right|=0$
$A_{31}=\left|\begin{array}{rr}-1 & 2 \\ 1 & 2\end{array}\right|=-4$
$A_{32}=-\left|\begin{array}{rr}3 & 2 \\ -2 & 2\end{array}\right|=-10$
$A_{33}=\left|\begin{array}{rr}3 & -1 \\ -2 & 1\end{array}\right|=1$
$\left[\begin{array}{rrr}6 & 14 & -1 \\ 2 & 6 & 0 \\ -4 & -10 & 1\end{array}\right]$
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