If for the matrix $A=\left[\begin{array}{cc}1 & -\alpha \ \alpha & \beta\end{array}\right], A A^{\top}=I_2$, then the value of $\alpha^4+\beta^4$ is: [JEE Main 2021, 25 Feb (Shift 2)]

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If for the matrix \(A=\left[\begin{array}{cc}1 & -\alpha \\ \alpha & \beta\end{array}\right], A A^{\top}=I_2\), …

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If for the matrix \(A=\left[\begin{array}{cc}1 &amp; -\alpha \\ \alpha &amp; \beta\end{array}\right], A A^{\top}=I_2\), …

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If for the matrix \(A=\left[\begin{array}{cc}1 & -\alpha \\ \alpha & \beta\end{array}\right], A A^{\top}=I_2\), …