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A + A^-1 or A - A^-1 for a 2x2 matrix

This type of question, asked 4 times: 20 Apr 2026 S1, 12 May 2026 S1, 19 May 2026 S1, 19 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    20 Apr 2026 S1

    67
    Let A=[a11b]A = \begin{bmatrix} a & 1 \\ 1 & b \end{bmatrix}, where aa and bb are the roots of the equation x2−4x+2=0x^2 - 4x + 2 = 0. If A+A−1=kI2A + A^{-1} = kI_2, then the value of kk is ____

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  2. Question 2

    12 May 2026 S1

    67
    If A=[sin⁡α−cos⁡αcos⁡αsin⁡α]A = \begin{bmatrix} \sin\alpha & -\cos\alpha \\ \cos\alpha & \sin\alpha \end{bmatrix} and S={α:α∈(π2,3π2),A+A−1=I}S = \left\{\alpha : \alpha \in \left(\dfrac{\pi}{2}, \dfrac{3\pi}{2}\right), A + A^{-1} = I\right\}, then α=\alpha = ...

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  3. Question 3

    19 May 2026 S1

    70
    If A=[2−35−7]A = \begin{bmatrix} 2 & -3 \\ 5 & -7 \end{bmatrix}, then A−A−1=A - A^{-1} =

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  4. Question 4

    19 May 2026 S2

    68
    The sum of the matrix [2−35−7]\begin{bmatrix} 2 & -3 \\ 5 & -7 \end{bmatrix} and its multiplicative inverse is

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