JEE MAIN - Mathematics (2024 - 29th January Morning Shift - No. 8)
$$\text { Let } A=\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & \alpha & \beta \\
0 & \beta & \alpha
\end{array}\right] \text { and }|2 \mathrm{~A}|^3=2^{21} \text { where } \alpha, \beta \in Z \text {, Then a value of } \alpha \text { is }$$
9
17
3
5
Explanation
$$\begin{aligned}
& |\mathrm{A}|=\alpha^2-\beta^2 \\
& |2 \mathrm{~A}|^3=2^{21} \Rightarrow|\mathrm{A}|=2^4 \\
& \alpha^2-\beta^2=16 \\
& (\alpha+\beta)(\alpha-\beta)=16 \Rightarrow \alpha=4 \text { or } 5
\end{aligned}$$
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