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Find unknown entries of A or A^-1 when both are given, using A A^-1 = I

This type of question, asked 8 times: 9 May 2023 S1, 22 Apr 2025 S2, 13 Apr 2026 S1, 18 Apr 2026 S2, 19 Apr 2026 S2, 12 May 2026 S2, 14 May 2026 S2, 15 May 2026 S2. All 8 questions below, oldest first.

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  1. Question 1

    9 May 2023 S1

    101
    If A=(1111a3322)A = \begin{pmatrix}1&1&1\\1&a&3\\3&2&2\end{pmatrix} and B=(−20b7−1−2c11)B = \begin{pmatrix}-2&0&b\\7&-1&-2\\c&1&1\end{pmatrix} and if matrix B is the inverse of matrix A, then value of 4a+2b−c4a+2b-c is

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  2. Question 2

    22 Apr 2025 S2

    109
    If matrix A=111[−17−242a42−315]A =\frac{1}{11}\begin{bmatrix} - 1 & 7 & - 24 \\ 2 & a & 4 \\ 2 & - 3 & 15 \end{bmatrix} and A−1=[3342−34b−1c]A^{- 1}=\begin{bmatrix} 3 & 3 & 4 \\ 2 & - 3 & 4 \\ b & - 1 & c \end{bmatrix}, then the values of a,b,ca,b,c respectively are ____\_\_\_\_

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  3. Question 3

    13 Apr 2026 S1

    67
    If A=[20−1510013]3×3A = \begin{bmatrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{bmatrix}_{3 \times 3}, and A−1=[γ−11α6−5β−22]3×3A^{-1} = \begin{bmatrix} \gamma & -1 & 1 \\ \alpha & 6 & -5 \\ \beta & -2 & 2 \end{bmatrix}_{3 \times 3}, then ∣α⋅β⋅γ∣=|\alpha \cdot \beta \cdot \gamma| = _____ (where ∣⋅∣|\cdot| denotes the absolute value)

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  4. Question 4

    18 Apr 2026 S2

    63
    If matrix A and its inverse A−1A^{-1} are given by A=[0121233x1]A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & x & 1 \end{bmatrix} and A−1=[12−1212−43y52−3212]A^{-1} = \begin{bmatrix} \dfrac{1}{2} & -\dfrac{1}{2} & \dfrac{1}{2} \\ -4 & 3 & y \\ \dfrac{5}{2} & -\dfrac{3}{2} & \dfrac{1}{2} \end{bmatrix}, then the polar co-ordinates of the points whose Cartesian co-ordinates are (x,y)(x, y) are …\ldots

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  5. Question 5

    19 Apr 2026 S2

    66
    The inverse of the matrix A=[2−144−31121]A = \begin{bmatrix} 2 & -1 & 4 \\ 4 & -3 & 1 \\ 1 & 2 & 1 \end{bmatrix} is B=137[−5911−3−21411−5k]B = \dfrac{1}{37}\begin{bmatrix} -5 & 9 & 11 \\ -3 & -2 & 14 \\ 11 & -5 & k \end{bmatrix}, then the value of kk is...

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  6. Question 6

    12 May 2026 S2

    68
    If the matrix A=[3−54−7]A = \begin{bmatrix} 3 & -5 \\ 4 & -7 \end{bmatrix} and A−1=[7−54a]A^{-1} = \begin{bmatrix} 7 & -5 \\ 4 & a \end{bmatrix}, then the value of aa is...

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  7. Question 7

    14 May 2026 S2

    71
    If the matrix A=[123115247]A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7 \end{bmatrix} and its inverse is A−1=[ac−7b−1c−201]A^{-1} = \begin{bmatrix} a & c & -7 \\ b & -1 & c \\ -2 & 0 & 1 \end{bmatrix}, then ....

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  8. Question 8

    15 May 2026 S2

    72
    If A=[0121233a1]A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix} and A−1=[12−1212−43c52−3212]A^{-1} = \begin{bmatrix} \dfrac{1}{2} & -\dfrac{1}{2} & \dfrac{1}{2} \\ -4 & 3 & c \\ \dfrac{5}{2} & -\dfrac{3}{2} & \dfrac{1}{2} \end{bmatrix}, then ...

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