we have $\mathrm{M}_{11}=\left|\begin{array}{cc}0 & 4 \\ 5 & -7\end{array}\right|=0-20=-20 ; \mathrm{A}_{11}=(-1)^{1+1}(-20)=-20$

$\mathrm{M}_{12}=\left|\begin{array}{cc}6 & 4 \\ 1 & -7\end{array}\right|=-42-4=-46 ; \quad \mathrm{A}_{12}=(-1)^{1+2}(-46)=46$

$\mathrm{M}_{13}=\left|\begin{array}{ll}6 & 0 \\ 1 & 5\end{array}\right|=30-0=30 ; \quad \mathrm{A}_{13}=(-1)^{1+3}(30)=30$

$\mathrm{M}_{21}=\left|\begin{array}{cc}-3 & 5 \\ 5 & -7\end{array}\right|=21-25=-4 ; \quad \mathrm{A}_{21}=(-1)^{2+1}(-4)=4$
$\mathrm{M}_{22}=\left|\begin{array}{cc}2 & 5 \\ 1 & -7\end{array}\right|=-14-5=-19 ; \quad \mathrm{A}_{22}= (-1)^{2+2}(-19)=-19$

$\mathrm{M}_{23}=\left|\begin{array}{cc}2 & -3 \\ 1 & 5\end{array}\right|=10+3=13 ; \quad \quad \mathrm{A}_{23}=(-1)^{2 * 3}(13)=-13$

$\mathrm{M}_{31}=\left|\begin{array}{cc}-3 & 5 \\ 0 & 4\end{array}\right|=-12-0=-12 ; \quad \mathrm{A}_{31}=(-1)^{3+1}(-12)=-12$

$M_{32}=\left|\begin{array}{ll}2 & 5 \\ 6 & 4\end{array}\right|=8-30=-22 ; \quad \quad A_{32}=(-1)^{3+2}(-22)=22$

and $\mathrm{M}_{33}=\left|\begin{array}{cc}2 & -3 \\ 6 & 0\end{array}\right|=0+18=18 ; \quad \quad \mathrm{A}_{33}=(-1)^{3+3}(18)=18$

Now $\quad a_{11}=2, a_{12}=-3, a_{13}=5 ; \mathrm{A}_{31}=-12, \mathrm{A}_{32}=22, \mathrm{A}_{33}=18$

So $\quad a_{11} A_{31}+a_{12} A_{32}+a_{13} A_{33}$

$=2(-12)+(-3)(22)+5(18)=-24-66+90=0$