Question

If $A$ is a square matrix such that $A\left(\text{adj}A\right)=\left(\begin{array}{ccc}4& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right),$ then value of $\text{det(adj}A)$ equals to

• A. $4$
• B. $16$
• C. $64$
• D. $256$

Answer 1

The correct option is B $16$

$A\left(\text{adj}A\right)=|A|.I=4I$
Then $|\text{adj}A|=|A{|}^{n-1}=4^{3-1}=16$, where order of matrix $A$ is $n=3$