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