If $A =\left[\begin{array}{cc}\sqrt{2} & 1 \ -1 & \sqrt{2}\end{array}\right], B =\left[\begin{array}{ll}1 & 0 \ 1 & 1\end{array}\right], C = ABA ^{ T }$ and $X = A ^{ T } C ^2 A$, then $\operatorname{det} X$ is equal to : [JEE Main 2024, 01 Feb (Shift 1)]

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If \(A =\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], B =\left[\begin{array}{ll}1 &amp…

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If \(A =\left[\begin{array}{cc}\sqrt{2} &amp; 1 \\ -1 &amp; \sqrt{2}\end{array}\right], B =\left[\begin{array}{ll}1 &amp…

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If \(A =\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], B =\left[\begin{array}{ll}1 &amp…