[ Let A=[[arraylll 1 & 0 & 0 0 & & 0 & & array]] and |2 ~A|^3=2^21 where , Z , Then a valu…

Question

$$\text { Let } A=\left[\[\begin{array}{lll} 1 & 0 & 0 \ 0 & \alpha & \beta \ 0 & \beta & \alpha \end{array}$$\right] \text { and }|2 \mathrm{~A}|\^3=2\^{21} \text { where } \alpha, \beta \in Z \text {, Then a value of } \alpha \text { is }\]

Accepted Answer

$$\begin{aligned}
& |\mathrm{A}|=\alpha^2-\beta^2 \
& |2 \mathrm{~A}|^3=2^{21} \Rightarrow|\mathrm{A}|=2^4 \
& \alpha^2-\beta^2=16 \
& (\alpha+\beta)(\alpha-\beta)=16 \Rightarrow \alpha=4 \text { or } 5
\end{aligned}$$

Solutions · 1