Question

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

(a) 14⁴
(b) 14³
(c) 14²
(d) 14

Answer 1

(a) 14⁴

$$\begin{gathered} \mathrm{Given}: \\ A=\left[12-1 \\ -112 \\ 2-11\right] \\ \therefore \left|A\right|=\left|12-1 \\ -112 \\ 2-11\right|=1\left(1+2\right)-2\left(-1-4\right)-1\left(1-2\right)=3+10+1=14 \\ \mathrm{We}\mathrm{have} \\ \left|\mathrm{adj}\left(\mathrm{adj}A\right)\right|={\left|A\right|}^{{\left(n-1\right)}^2} \\ \Rightarrow \left|\mathrm{adj}\left(\mathrm{adj}A\right)\right|={\left(14\right)}^{2^2}={14}^4 \end{gathered}$$