Answer
$det(A)=-58$
Work Step by Step
$ \begin{bmatrix}
1 & 4 & -2 \\
3 & 2 & 0 \\
-1 & 4 & 3
\end{bmatrix} $
$M_{11}= \begin{bmatrix}
2 &0 \\
4& 3\\
\end{bmatrix} = 2\times3-4(0)=6$
$M_{12}= \begin{bmatrix}
3 &0 \\
-1& 3\\
\end{bmatrix}=3\times3-(-1)0=9$
$M_{13}= \begin{bmatrix}
3 &2 \\
-1& 4\\
\end{bmatrix}= 3\times4-(-1)2=14$
To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$
$C_{11}=6$
$C_{12}=-9$
$C_{13}=14$
$det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$
$det(A)=1\times6+4\times(-9)-2\times14$
$det(A)=-58$