Answer
$\det(A)=-892$
Work Step by Step
Use the Cofactor ExpansionTheorem along column 1:
$\det(A)=a_{11}C_{11}+a_{21}C_{21}+a_{31}C_{31}$
where $C_{ij}=(_1)^{i+j}.M_{ij}$
Hence, the the determinant is:
$\det(A)=2\begin{vmatrix} 5 & -3 & 7
\\ 2&6 &3 \\
2 & -4 & 5 \\
\end{vmatrix}-(-7)\begin{vmatrix} 5 &-3 &7
\\ 6 & 6 &3 \\
4 & -4 &5
\end{vmatrix}+4\begin{vmatrix} 5 &5 & 7
\\ 6 & 2 &3\\
4 & 2 &5
\end{vmatrix}-3\begin{vmatrix} 5 &5 & -3
\\ 6 & 2 &6 \\
4 & 2 & -4
\end{vmatrix}$
$\det (A)=2.[5.42+3.4+7.(-20)]+7.[5.42+3.18+7.(-48)]+4.(5.4-5.18+7.4)-3.[5.(-20)-5.(-48)-3.4]$
$\det (A)=164-504-168-384$
$\det(A)=-892$
