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Use A(adj A) = |A| I

This type of question, asked 2 times: May 2021 S1, May 2022 S1. All 2 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    116
    For an invertible matrix AA, if A(adj A)=(200020)A(\text{adj}\,A) = \begin{pmatrix}20 & 0\\0 & 20\end{pmatrix}, then ∣A∣=|A| =

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  2. Question 2

    May 2022 S1

    139
    Given A=(x321y422z)A = \begin{pmatrix} x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z \end{pmatrix}, if xyz=60xyz = 60 and 8x+4y+3z=208x + 4y + 3z = 20, then A(adj A)A(\text{adj}\,A)

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