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Find the power of A that equals A^-1 (A^k = I)

This type of question, asked 3 times: 11 May 2024 S2, 25 Apr 2025 S1, 11 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    11 May 2024 S2

    144
    If A=(i110)A=\begin{pmatrix}i&1\\1&0\end{pmatrix} where i=−1i=\sqrt{-1} and B=A2029B=A^{2029}, then B−1=B^{-1}=

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  2. Question 2

    25 Apr 2025 S1

    120
    If A=[3−342−340−11]3×3A=\begin{bmatrix} 3 & - 3 & 4 \\ 2 & - 3 & 4 \\ 0 & - 1 & 1 \end{bmatrix}_{3 \times 3}, then A−1=A^{- 1}=

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  3. Question 3

    11 Apr 2026 S2

    65
    If A=[00−10−10−100]A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix} then which of the following is true ?

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