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

Question

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

Accepted Answer

Answer: D. 5 \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 	ext { or } 5 \end{aligned}

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

Answer

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