Question

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

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

Answer 1

Answer: (B)

$3^2\times 2^8$

$\left|A\right|=6$

$\left|2A\right|=2^3\left|A\right|=2^3\times 6=2^4\times 3$

$\left|adj2A\right|={\left|2A\right|}^{3-1}={\left(2^4\times 3\right)}^2=2^8\times 3^2$