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Matrices and Determinants question

2024 · 1 Feb · Shift 1 · Q33

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JEE Main
Mathematics
Matrices and Determinants
2024 · 1 Feb · Shift 1 · Q33

Matrices and Determinants question

2024 · 1 Feb · Shift 1 · Q33

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

If

\mathrm{A}=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], \mathrm{C}=\mathrm{ABA}^{\mathrm{T}}

and

\mathrm{X}=\mathrm{A}^{\mathrm{T}} \mathrm{C}^2 \mathrm{~A}

, then

\operatorname{det} \mathrm{X}

is equal to :

A
243
B
729
C
27
D
891

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