Let $A=\left[\begin{array}{lll}1 & 0 & 0 \ 0 & \alpha & \beta \ 0 & \beta & \alpha\end{array}\right]$ and $|2 A|^{3}=2^{21}$ where $\alpha, \beta \in Z$, Then a value of $\alpha$ is [JEE Main 2024, 29 Jan (Shift 1)]

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Let \(A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}…

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Let \(A=\left[\begin{array}{lll}1 &amp; 0 &amp; 0 \\ 0 &amp; \alpha &amp; \beta \\ 0 &amp; \beta &amp; \alpha\end{array}…

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Let \(A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}…