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Matrices and Determinants question

2023 · 25 Jan · Shift 2 · Q36

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JEE Main
Mathematics
Matrices and Determinants
2023 · 25 Jan · Shift 2 · Q36

Matrices and Determinants question

2023 · 25 Jan · Shift 2 · Q36

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let

A = \left[ {\begin{matrix} {{1 \over {\sqrt {10} }}} & {{3 \over {\sqrt {10} }}} \\ {{{ - 3} \over {\sqrt {10} }}} & {{1 \over {\sqrt {10} }}} \\ \end{matrix} } \right]

and

B = \left[ {\begin{matrix} 1 & { - i} \\ 0 & 1 \\ \end{matrix} } \right]

, where

i = \sqrt { - 1}

. If

\mathrm{M=A^T B A}

, then the inverse of the matrix

\mathrm{AM^{2023}A^T}

is

A
$\left[ {\begin{matrix} 1 & { - 2023i} \\ 0 & 1 \\ \end{matrix} } \right]$
B
$\left[ {\begin{matrix} 1 & 0 \\ {2023i} & 1 \\ \end{matrix} } \right]$
C
$\left[ {\begin{matrix} 1 & {2023i} \\ 0 & 1 \\ \end{matrix} } \right]$
D
$\left[ {\begin{matrix} 1 & 0 \\ { - 2023i} & 1 \\ \end{matrix} } \right]$

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