Question

If $A=\left[\begin{array}{ccc}3& -3& 4\\ 2& -3& 4\\ 0& -1& 1\end{array}\right]$ , $B=(adjA)$ and $C=5A$ then $\frac{|C|}{|adjB|}$ is equal to

• A. 125
• B. -1
• C. 5
• D. -5

Answer 1

Answer: (A)

$A=\left[\begin{array}{ccc}3& -3& 4\\ 2& -3& 4\\ 0& -1& 1\end{array}\right],|A|=3\{(-3)+4\}3.(2)+4(-2)=3+6-8=1$ ...(i)
Given, $B=adjA,C=5A$
$|C|=|5A|=5^3|A|=5^3=125$ (From (i))
Also, $[adjB|=[adj(adjA)|=|A{|}^{(3-1{)}^2}=|A{|}^4$
$\therefore \frac{|C|}{|adjB|}=\frac{125}{|adj\left(adjA\right)|}=\frac{125}{{|A|}^4}=125(\because |A|=1)$