If $A = \frac{1}{\sqrt{5}} \begin{pmatrix} 1 & 2 \ -2 & 1 \end{pmatrix}$, $B = \begin{pmatrix} 1 & i \ i & 1 \end{pmatrix}$, $i = \sqrt{-1}$, and $Q = ABA^T$, then the inverse of the matrix $A Q^{2021} A^T$ is equal to :

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$\begin{pmatrix} 1 & -2021i \ 2021i & 1 \end{pmatrix}$

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If $A = \frac{1}{\sqrt{5}} \begin{pmatrix} 1 & 2 \\ -2 & 1 \end{pmatrix}$ , $B = \begin{pmatrix} 1 & i \\ i & 1 \end{pmatrix}$ , $i = \sqrt{-1}$ , and $Q = ABA^T$ , then the inverse of the matrix $A Q^{2021} A^T$ is equal to :

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