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JEE Main 2023 · 25 Jan · Shift 2

JEE Main 2023 Mathematics question on Matrices and Determinants

Let A=[110310−310110]A = \begin{bmatrix} \frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}} \end{bmatrix} and B=[1−i01]B = \begin{bmatrix} 1 & -i \\ 0 & 1 \end{bmatrix}, where i=−1i = \sqrt{-1}.

If M=ATBAM = A^T B A, then the inverse of the matrix AM2023ATAM^{2023}A^T is
  1. A.
    [1−2023i01]\begin{bmatrix} 1 & -2023i \\ 0 & 1 \end{bmatrix}
  2. B.
    [12023i01]\begin{bmatrix} 1 & 2023i \\ 0 & 1 \end{bmatrix}
  3. C.
    [102023i1]\begin{bmatrix} 1 & 0 \\ 2023i & 1 \end{bmatrix}
  4. D.
    [10−2023i1]\begin{bmatrix} 1 & 0 \\ -2023i & 1 \end{bmatrix}
Show answer

Correct option: A

[JEE Main 2023 · 25 Jan · Shift 2]

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