Question

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

• A. $a^3$
• B. $a^6$
• C. $a^9$
• D. a

Answer 1

The correct option is C $a^9$

$A=\left[\begin{array}{ccc}a& 0& 0\\ 0& a& 0\\ 0& 0& a\end{array}\right]$

$\left(A\right)=\left[\begin{array}{ccc}{a}^2& 0& 0\\ 0& a^2& 0\\ 0& 0& a^2\end{array}\right]Adj\left(A\right)=\left[\begin{array}{ccc}{a}^2& 0& 0\\ 0& a^2& 0\\ 0& 0& a^2\end{array}\right]$

$|A|=a^3$

$|Adj\left(A\right)|=a^6$

$|A|.|Adj\left(A\right)|=a^3{a}^6=a^9$

$C$ is correct