Question

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

• A. $(14{)}^1$
• B. $(14{)}^2$
• C. $(14{)}^3$
• D. $(14{)}^4$

Answer 1

The correct option is D $(14{)}^4$

$A=\left[\begin{array}{ccc}1& 2& -1\\ -1& 1& 2\\ 2& -1& 1\end{array}\right]$
We know that
$|adjA|={|A|}^{n-1}$
Here, $|A|=1(1+2)-2(-1-4)-(-1-2)=14$
det $\left(adj\right(adjA\left)\right)=|A{|}^{{(3-1)}^2}={\left(14\right)}^4$