Question

If $A=\left[\begin{array}{ccc}1& 2& -1\\ -1& 1& 2\\ 2& -1& 1\end{array}\right]$, then det$\left(adj\left(adjA\right)\right)$, is

• A. ${14}^4$
• B. ${14}^3$
• C. ${14}^2$
• D. $14$

Answer 1

The correct option is A ${14}^4$

Given $A=\left[\begin{array}{ccc}1& 2& -1\\ -1& 1& 2\\ 2& -1& 1\end{array}\right]$
$\Rightarrow |A|=1(1+2)-2(-1-4)-1(1-2)=14$
$|adj\left(adjA\right)|=|A{|}^{(n-1{)}^2}$

$\Rightarrow |adj\left(adjA\right)|=(14{)}^4$