Question

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

• A. $(14{)}^4$
• B. $(14{)}^6$
• C. $(14{)}^9$
• D. $(14{)}^2$

Answer 1

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

$|A|=(1+2)-2(-1-4)-1(1-2)$
$=3+10+1=14$
$\therefore det\left(Adj\right(AdjA\left)\right)=|AdjA{|}^2=|A{|}^4=(14{)}^4$