Mathematics - Matrices Question with Solution | TestHub

$\left|A\right|=\left|\begin{array}{ccc}1& 1& 2\\ 1& 3& 4\\ 1& -1& 3\end{array}\right|=\left(\left(9+4\right)-1\left(3-4\right)+2\left(-1-3\right)\right)=13+1-8=6$
$\left|adjB\right|=\left|adjadjA\right|={\left|A\right|}^{{\left(n-1\right)}^2}={\left|A\right|}^4={\left(36\right)}^2$
$\left|C\right|=\left|3A\right|=3^3\times 6$
$\frac{\left|adjB\right|}{\left|C\right|}=\frac{36\times 36}{3^3\times 6}=8$