Let A= [1/(√ 10), 3/(√ 10); -3/(√ 10), 1/(√ 10)] and B= [1, -i; 0, 1], where i=√ -1. If M=A^T B A, then the inverse of the matrix A M^2023 A^T is

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