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Mathematics Question on Matrices

Let A=[110310 −310110]A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right] and B=[1−i 01]B=\left[\begin{array}{cc}1 & -i \\\ 0 & 1\end{array}\right], where i=−1i=\sqrt{-1} If M=ATBAM = A ^{ T } B A, then the inverse of the matrix AM2023ATAM ^{2023} A ^{ T } is

A

[1−2023i 01]\begin{bmatrix}1 & -2023 i \\\ 0 & 1\end{bmatrix}

B

[10 2023i1]\begin{bmatrix}1 & 0 \\\ 2023 i & 1\end{bmatrix}

C

[12023i 01]\begin{bmatrix}1 & 2023 i \\\ 0 & 1\end{bmatrix}

D

[10 −2023i1]\begin{bmatrix}1 & 0 \\\ -2023 i & 1\end{bmatrix}

Answer

[12023i 01]\begin{bmatrix}1 & 2023 i \\\ 0 & 1\end{bmatrix}

Explanation

Solution

The correct answer is [12023i 01]\begin{bmatrix}1 & 2023 i \\\ 0 & 1\end{bmatrix}