Question

If the matrices $A=\left[\begin{array}{ccc}1& 1& 2\\ 1& 3& 4\\ 1& -1& 3\end{array}\right]$, B = adj A and C = 3A , then $\frac{|adjB|}{|C|}$ is equal to :

• A. 16
• B. 2
• C. 8
• D. 72

Answer 1

Answer: (C)

$A=\left[\begin{array}{ccc}1& 1& 2\\ 1& 3& 4\\ 1& -1& 3\end{array}\right]$
$\Rightarrow \left|A\right|=6$
$\frac{|adjB|}{|c|}=\frac{|adj\left(adjA\right)|}{|9A|}=\frac{{|A|}^4}{3^3|A|}=\frac{{|A|}^3}{3^3}$
$=\frac{{\left(6\right)}^3}{{\left(3\right)}^3}=8$