JEE Math Practice Question

If $$A = \left( {\begin{matrix} {{1 \over {\sqrt 5 }}} & {{2 \over {\sqrt 5 }}} \\ {{{ - 2} \over {\sqrt 5 }}} & {{1 \over {\sqrt 5 }}} \\ \end{matrix} } \right)$$, $$B = \left( {\begin{matrix} 1 & 0 \\ i & 1 \\ \end{matrix} } \right)$$, $$i = \sqrt { - 1} $$, and Q = ATBA, then the inverse of the matrix A Q2021 AT is equal to :

1. A.$$\left( {\begin{matrix} {{1 \over {\sqrt 5 }}} & { - 2021} \\ {2021} & {{1 \over {\sqrt 5 }}} \\ \end{matrix} } \right)$$
2. B.$$\left( {\begin{matrix} 1 & 0 \\ { - 2021i} & 1 \\ \end{matrix} } \right)$$
3. C.$$\left( {\begin{matrix} 1 & 0 \\ {2021i} & 1 \\ \end{matrix} } \right)$$
4. D.$$\left( {\begin{matrix} 1 & { - 2021i} \\ 0 & 1 \\ \end{matrix} } \right)$$