Let A = [{1/√10 3/√10} {-3/√10 1/√10}] and B = [{1 -i} {0 1}], where i = √-1.

Question

Let \(A = \begin{bmatrix} \frac 1{\sqrt{10}}&\frac 3{\sqrt{10}}\\\frac {-3}{\sqrt{10}}&\frac 1{\sqrt{10}}\end{bmatrix}\) and \(B = \begin{bmatrix} 1&-i\\0&1\end{bmatrix}\), where i = √-1. If M = A^TBA, then the inverse of the matrix AM²⁰²³A^T is

(1) \(\begin{bmatrix}1&{-2023i}\\0&1\end{bmatrix}\)

(2) \(\begin{bmatrix}1&0\\{-2023i}&1\end{bmatrix}\)

(3) \(\begin{bmatrix}1&0\\{2023i}&1\end{bmatrix}\)

(4) \(\begin{bmatrix}1&{2023i}\\0&1\end{bmatrix}\)

Answer 1

Correct option is (4) \(\begin{bmatrix}1&{2023i}\\0&1\end{bmatrix}\)