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Matrices and Determinants question

2025 · 2 Apr · Shift 1 · Q26

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JEE Main
Mathematics
Matrices and Determinants
2025 · 2 Apr · Shift 1 · Q26

Matrices and Determinants question

2025 · 2 Apr · Shift 1 · Q26

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let

\mathrm{A}=\left[\begin{array}{cc}\alpha & -1 \\ 6 & \beta\end{array}\right], \alpha\gt 0

, such that

\operatorname{det}(\mathrm{A})=0

and

\alpha+\beta=1

. If I denotes

2 \times 2

identity matrix, then the matrix

(I+A)^8

is :

A
$\left[\begin{array}{cc}257 & -64 \\ 514 & -127\end{array}\right]$
B
$\left[\begin{array}{cc}766 & -255 \\ 1530 & -509\end{array}\right]$
C
$\left[\begin{array}{cc}1025 & -511 \\ 2024 & -1024\end{array}\right]$
D
$\left[\begin{array}{ll}4 & -1 \\ 6 & -1\end{array}\right]$

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