Answer
$det(A)=-66$
Work Step by Step
$ \begin{bmatrix}
-3 & 0 & 0 \\
7 & 11 & 0 \\
1& 2 & 2
\end{bmatrix} $
$M_{11}= \begin{bmatrix}
11 &0 \\
2& 2\\
\end{bmatrix} = 11\times2-2\times0=22$
$M_{12}= \begin{bmatrix}
7 &0 \\
1& 2\\
\end{bmatrix}=7\times2-1\times0=14$
$M_{13}= \begin{bmatrix}
7 &11 \\
1& 2\\
\end{bmatrix}= 7\times2-1\times11=3$
To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$
$C_{11}=22$
$C_{12}=-14$
$C_{13}=3$
$det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$
$det(A)=-3\times22+0\times(-14)+0\times3$
$det(A)=-66$
