Question

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

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

Answer 1

Answer: (B)

$16$

$A\left(AdjA\right)=\left(\begin{array}{ccc}4& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right)=|A|I$
$\Rightarrow 4\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]=|A|I$
$\therefore |A|=4$
det (Adj A) $=|A{|}^{n-1}$, where $n$ is number of rows in a matrix
$=|4{|}^{3-1}$
$=16$.
so (b) is answer.