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A = [1, tan x; -tan x, 1]: find A^T A^-1

The same question, asked 2 times: 13 May 2024 S2, 20 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    13 May 2024 S2

    126
    If A=(1tan⁡x−tan⁡x1)A=\begin{pmatrix}1 & \tan x\\ -\tan x & 1\end{pmatrix}, then ATA−1=A^T A^{-1}=

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  2. Question 2

    20 Apr 2025 S1

    148
    If A=[1tan⁡x−tan⁡x1]A =\begin{bmatrix} 1 & \tan x \\ - \tan x & 1 \end{bmatrix}, then ATA−1=A^{T}A^{- 1}=

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