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

Question

$$\left[ {\matrix{ 1 & { - 2023i} \cr 0 & 1 \cr } } \right]$$

$$\left[ {\matrix{ 1 & 0 \cr {2023i} & 1 \cr } } \right]$$

$$\left[ {\matrix{ 1 & {2023i} \cr 0 & 1 \cr } } \right]$$

$$\left[ {\matrix{ 1 & 0 \cr { - 2023i} & 1 \cr } } \right]$$

Solution

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