Question

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

• A. $a^9$
• B. $a^3$
• C. $a$
• D. $1$

Answer 1

The correct option is A $a^9$

$|A||adjA|=|AadjA|=||A|I|$
$=|A{|}^3=(a^3{)}^3=a^9$