Question

If $A$ is a square matrix such that $A\left(AdjA\right)=\left(\begin{array}{ccc}4& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right)$ then det $\left(AdjA\right)=$

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

Answer 1

The correct option is B $16$

$A^{-1}=\frac{adjA}{|A|}$

$A{A}^{-1}=\frac{AadjA}{|A|}$

$I=\frac{AadjA}{|A|}$

$AadjA=I|A|$

ATQ :

$|A|I=4\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

$|A|=4$

$\left[AadjA\right]=|A{|}^{n-1}=|A{|}^{3-1}=|A{|}^2=4^2=16$