Question

If $A=\left[\begin{array}{ccc}a& 0& 0\\ 0& a& 0\\ 0& 0& a\end{array}\right]$, then the value of $\left|adjA\right|$, is

• A. $a^{27}$
• B. $a^9$
• C. $a^6$
• D. $a^2$

Answer 1

The correct option is C $a^6$

$A=\left[\begin{array}{ccc}a& 0& 0\\ 0& a& 0\\ 0& 0& a\end{array}\right]$
$|A|=a^3$
Now, $|adjA|=|A{|}^{n-1}$
$\therefore |adjA|=(a^3{)}^2=a^6$