Question

For a $3\times 3$ matrix $A$, if $\left|A\right|=4$ then $\left|\text{adj}A\right|$ equals

• A. $-4$
• B. $4$
• C. $16$
• D. $64$

Answer 1

The correct option is C $16$

$\left|AdjA\right|={\left|A\right|}^{n-1}$

$\Rightarrow \left|AdjA\right|={\left(4\right)}^{3-1}$

$\left|AdjA\right|=4^2=16$

Option C