Question

If det$\left(A_{3\times 3}\right)=6$, then det $\left(adj2A\right)=?$

• A. $144$
• B. $24$
• C. $3^3\times 2^4$
• D. $3^2\times 2^8$

Answer 1

Answer: (B)

$24$

$\begin{array}{c}Let\left(A_3\times 3\right)=6,then\left(\frac{ced}{2A}\right)=?\\ \Rightarrow \left|A\right|=6\left(given\right)\\ \Rightarrow Then,\left|\frac{AD}{2A}\right|={\left|2A\right|}^{n-1}={\left|2A\right|}^{3-n}={\left|2A\right|}^2=2^2\left|A\right|\\ =4\times 6=24\end{array}$