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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 \( Q = A ^{ T } BA \), then the inverse of \( A Q ^{2021} A ^{ T } \) is equal to : Options: \[ \begin{array}{l} \text { 86435166739. } \\ \text { 86435166740. } \\ \left(\begin{array}{ccc} 1 & 0 \\ -2021 & i & 1 \end{array}\right) \\ \left.\begin{array}{cc} \frac{1}{\sqrt{5}} & -2021 \\ 2021 & \frac{1}{\sqrt{5}} \end{array}\right) \end{array} \] \[ \begin{array}{l} \text { 86435166741. } \\ \text { 86435166742. } \\ \left(\begin{array}{ccc} 1 & -2021 & i \\ 0 & 1 & 0 \\ 2021 & i & 1 \end{array}\right) \end{array} \]

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