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MCQMediumJEE Main 2025 · 2 April, Shift 1Algebra of Matrices

Mathematics Question from JEE Main 2025 · 2 April, Shift 1

Let A=[α−16β], α>0A = \begin{bmatrix} \alpha & -1 \\ 6 & \beta \end{bmatrix},\ \alpha > 0, such that det⁡(A)=0\det(A) = 0 and α+β=1\alpha + \beta = 1. If II denotes the 2×22 \times 2 identity matrix, then the matrix (I+A)8(I + A)^8 is:

  • A

    [4−16−1]\begin{bmatrix} 4 & -1 \\ 6 & -1 \end{bmatrix}

  • B

    [257−64514−127]\begin{bmatrix} 257 & -64 \\ 514 & -127 \end{bmatrix}

  • C

    [1025−5112024−1024]\begin{bmatrix} 1025 & -511 \\ 2024 & -1024 \end{bmatrix}

  • D

    [766−2551530−509]\begin{bmatrix} 766 & -255 \\ 1530 & -509 \end{bmatrix}

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