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JEE Main 2021
26-08-2021 S1
Question
If $A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{ll}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}$, and $Q=A^{\top} B A$, then the inverse of the matrix $A Q^{2021} A^{\top}$ is equal to :
Select the correct option:
A
$\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & -2021 \\ 2021 & \frac{1}{\sqrt{5}}\end{array}\right)$
B
$\left(\begin{array}{cc}1 & 0 \\ -2021 i & 1\end{array}\right)$
C
$\left(\begin{array}{cc}1 & 0 \\ 2021 \mathrm{i} & 1\end{array}\right)$
D
$\left(\begin{array}{cc}1 & -2021 i \\ 0 & 1\end{array}\right)$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
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JEE Main
Mathematics
Hard
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