Question

If $A$ is a $3\times 3$ matrix and $|adjA|=16$ then $|A|=$

• A. $4$
• B. $-4$
• C. $\pm 4$
• D. $8$

Answer 1

Answer: (C)

$\pm 4$

$\left|adjA\right|=16$

$\Rightarrow {\left|A\right|}^{3-1}=16$

$\Rightarrow {\left|A\right|}^2=16$

$\left|A\right|=\pm 4$