JEE Math Practice Question

Let $$A = \left[ {\begin{matrix} {{1 \over {\sqrt {10} }}} & {{3 \over {\sqrt {10} }}} \\ {{{ - 3} \over {\sqrt {10} }}} & {{1 \over {\sqrt {10} }}} \\ \end{matrix} } \right]$$ and $$B = \left[ {\begin{matrix} 1 & { - i} \\ 0 & 1 \\ \end{matrix} } \right]$$, where $$i = \sqrt { - 1} $$. If $$\mathrm{M=A^T B A}$$, then the inverse of the matrix $$\mathrm{AM^{2023}A^T}$$ is

1. A.$$\left[ {\begin{matrix} 1 & { - 2023i} \\ 0 & 1 \\ \end{matrix} } \right]$$
2. B.$$\left[ {\begin{matrix} 1 & 0 \\ {2023i} & 1 \\ \end{matrix} } \right]$$
3. C.$$\left[ {\begin{matrix} 1 & {2023i} \\ 0 & 1 \\ \end{matrix} } \right]$$
4. D.$$\left[ {\begin{matrix} 1 & 0 \\ { - 2023i} & 1 \\ \end{matrix} } \right]$$