$$det(\left(\begin{matrix}-1&5&-7\\2&-3&9\\-2&-1&-8\end{matrix}\right))$$

$$\left(\begin{matrix}-1&5&-7&-1&5\\2&-3&9&2&-3\\-2&-1&-8&-2&-1\end{matrix}\right)$$

$$-\left(-3\right)\left(-8\right)+5\times 9\left(-2\right)-7\times 2\left(-1\right)=-100$$

$$-2\left(-3\right)\left(-7\right)-9\left(-1\right)-8\times 2\times 5=-113$$

$$-100-\left(-113\right)$$

$$13$$

$$det(\left(\begin{matrix}-1&5&-7\\2&-3&9\\-2&-1&-8\end{matrix}\right))$$

$$-det(\left(\begin{matrix}-3&9\\-1&-8\end{matrix}\right))-5det(\left(\begin{matrix}2&9\\-2&-8\end{matrix}\right))-7det(\left(\begin{matrix}2&-3\\-2&-1\end{matrix}\right))$$

$$-\left(-3\left(-8\right)-\left(-9\right)\right)-5\left(2\left(-8\right)-\left(-2\times 9\right)\right)-7\left(2\left(-1\right)-\left(-2\left(-3\right)\right)\right)$$

$$-33-5\times 2-7\left(-8\right)$$

$$13$$

$A_{11}=\left|\begin{array}{rr}-3 & 9 \\ -1 & -8\end{array}\right|=33$

$A_{12}=-\left|\begin{array}{rr}2 & 9 \\ -2 & -8\end{array}\right|=-2$

$A_{13}=\left|\begin{array}{rr}2 & -3 \\ -2 & -1\end{array}\right|=-8$

$A_{21}=-\left|\begin{array}{rr}5 & -7 \\ -1 & -8\end{array}\right|=47$

$A_{22}=\left|\begin{array}{rr}-1 & -7 \\ -2 & -8\end{array}\right|=-6$

$A_{23}=-\left|\begin{array}{rr}-1 & 5 \\ -2 & -1\end{array}\right|=-11$

$A_{31}=\left|\begin{array}{rr}5 & -7 \\ -3 & 9\end{array}\right|=24$

$A_{32}=-\left|\begin{array}{rr}-1 & -7 \\ 2 & 9\end{array}\right|=-5$

$A_{33}=\left|\begin{array}{rr}-1 & 5 \\ 2 & -3\end{array}\right|=-7$

$\left[\begin{array}{rrr}33 & -2 & -8 \\ 47 & -6 & -11 \\ 24 & -5 & -7\end{array}\right]$

$\left[\begin{array}{rrr}33 & 47 & 24 \\ -2 & -6 & -5 \\ -8 & -11 & -7\end{array}\right]$