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Cofactors and the adjoint of a given matrix

This type of question, asked 4 times: 9 May 2023 S2, 21 Apr 2025 S1, 19 Apr 2026 S1, 20 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    9 May 2023 S2

    113
    For the matrix A=(20−1312−112)A = \begin{pmatrix} 2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2 \end{pmatrix}, the matrix of cofactors is

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  2. Question 2

    21 Apr 2025 S1

    129
    The third element in the second row of adjoint of a matrix A=[aij]3×3A =\left\lbrack a_{ij} \right\rbrack_{3 \times 3} (where aij=2i+ja_{ij}= 2i + j ) is

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  3. Question 3

    19 Apr 2026 S1

    66
    If A=[aij]3×3A = [a_{ij}]_{3 \times 3}, where aij={1,if i+j is even0,if i+j is odda_{ij} = \begin{cases} 1, & \text{if } i + j \text{ is even} \\ 0, & \text{if } i + j \text{ is odd} \end{cases}, then adj(A)=…\mathrm{adj}(A) = \ldots

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  4. Question 4

    20 Apr 2026 S2

    65
    Let A=[312120114]A = \begin{bmatrix} 3 & 1 & 2 \\ 1 & 2 & 0 \\ 1 & 1 & 4 \end{bmatrix} and pC11+4C21−5C32=−2pC_{11} + 4C_{21} - 5C_{32} = -2, where CijC_{ij} denotes the cofactor of an element aija_{ij} of matrix AA, then the value of pp is :

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