$$A= \left[\begin{matrix} 1 & -1 & 2 \\3 & -2 & 2 \\2 & 1 & 1 \end{matrix}\right]$$
$A≔\left(\begin{matrix}1&-1&2\\3&-2&2\\2&1&1\end{matrix}\right)$
$\left[\begin{array}{rrr}-4 & 3 & 2 \\ 1 & -3 & 4 \\ 7 & -3 & 1\end{array}\right]$
$A_{11}=\left|\begin{array}{rr}-2 & 2 \\ 1 & 1\end{array}\right|=-4$
$A_{12}=-\left|\begin{array}{rr}3 & 2 \\ 2 & 1\end{array}\right|=1$
$A_{13}=\left|\begin{array}{rr}3 & -2 \\ 2 & 1\end{array}\right|=7$
$A_{21}=-\left|\begin{array}{rr}-1 & 2 \\ 1 & 1\end{array}\right|=3$
$A_{22}=\left|\begin{array}{rr}1 & 2 \\ 2 & 1\end{array}\right|=-3$
$A_{23}=-\left|\begin{array}{rr}1 & -1 \\ 2 & 1\end{array}\right|=-3$
$A_{31}=\left|\begin{array}{rr}-1 & 2 \\ -2 & 2\end{array}\right|=2$
$A_{32}=-\left|\begin{array}{rr}1 & 2 \\ 3 & 2\end{array}\right|=4$
$A_{33}=\left|\begin{array}{rr}1 & -1 \\ 3 & -2\end{array}\right|=1$
$\left[\begin{array}{rrr}-4 & 1 & 7 \\ 3 & -3 & -3 \\ 2 & 4 & 1\end{array}\right]$
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