The sum of the minor and the cofactor of the element 6 in the determinant $\Delta=\left|\begin{array}{lll}2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right|$ is :

0

$\Delta=\left|\begin{array}{lll}2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right|$

$M_{23}=\left|\begin{array}{ll}2 & 3 \\ 7 & 8\end{array}\right|=8 \times 2-7 \times 3$

$M_{23}=|6 - 2|$

$M_{23}=-5$  (Minor of 6)

(Co factor of 6)  C₂₃ = $(-1)^{2+3} M_{23}=-1 \times -5$

C₂₃ = 5

$M_{23}+C_{23}=5-5=0$