Answer
$\det(A)=11997$
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:
$\det(A)=3\begin{vmatrix} 3 &5 & -5
\\ 5 &-3 &-16 \\
-6 & 27 & -12 \\
\end{vmatrix}-5\begin{vmatrix} 2 &5 & -5
\\ 7 & -3 &-16 \\
9 & 27 &-12
\end{vmatrix}+2\begin{vmatrix} 2 &3 & -5
\\ 7 & 5 &-16 \\
9 & -6 &-12
\end{vmatrix}-6\begin{vmatrix} 2 &3 & 5
\\ 7 & 5 &-3 \\
9 & -6 &27
\end{vmatrix}$
$\det (A)=3.[3.468-5.(-156)-5.117]-5.(2.468-5.60-5.216)+2.[2.(-156)-3.60-5.(-87)]-6.[2.117-3.216+5.(-87)]$
$\det (A)=4797+2220-114+5094$
$\det(A)=11997$
