Mathematics · 2021
JEE Main · 26 August 2021, Shift 1 · Q63
If A = (1/(√ 5), 2/(√ 5); -2/(√ 5), 1/(√ 5)), B = (1, 0; i, 1), i=√ -1, and Q = A^T BA, then the inverse of the matrix A Q^2021 A^T is equal to:
If $\displaystyle \mathrm{A}=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), \mathrm{B}=\left(\begin{array}{cc}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}$, and $\displaystyle \mathrm{Q}=\mathrm{A}^{\mathrm{T}} \mathrm{BA}$, then the inverse of the matrix A $\displaystyle \mathrm{Q}^{2021} \mathrm{~A}^{\mathrm{T}}$ is equal to :
Official answer
(1)
$\displaystyle \left(\begin{array}{cc}
1 & 0 \\
-2021 i & 1
\end{array}\right)$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.