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A = [5a, -b; 3, 2] and A(adj A) = A A^T: find 5a + b

The same question, asked 4 times: 15 May 2023 S2, 12 May 2024 S2*, 25 Apr 2025 S2, 16 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    15 May 2023 S2

    117
    If A=(5a−b32)A = \begin{pmatrix} 5a & -b \\ 3 & 2 \end{pmatrix} and A⋅adj A=AATA \cdot \text{adj}\,A = AA^T, then 5a+b5a+b is equal to

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  2. Question 2

    12 May 2024 S2

    139
    If A=(2a−3b32)A = \begin{pmatrix}2a & -3b \\ 3 & 2\end{pmatrix} and A⋅adj A=AATA \cdot \text{adj}\, A = A A^T, then 2a+3b2a+3b is

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  3. Question 3

    25 Apr 2025 S2

    106
    If A=[5a−b32]A=\begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix} and A⋅adjA=AATA\cdot adjA=AA^{T}, then 5a+b=5a+b=

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  4. Question 4

    16 Apr 2026 S1

    65
    If A=[5a−b32]A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix} and A (adj A)=AATA\,(\mathrm{adj}\,A) = AA^T, then 5a+b=5a + b =

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