Let $\mathrm{A}=\left[\begin{matrix}\alpha & -1 \ 6 & \beta \end{matrix}\right],\alpha 0$, such that $\det (A)=0$ and $\alpha +\beta =1$. If $I$ denotes $2\times 2$ identity matrix, then the matrix $(I+\mathrm{A}{)}^{8}$ is: [JEE Main 2025, 2 Apr (Shift 1)]

Question

Let $\mathrm{A}=\left[\begin{matrix}\alpha & -1 \ 6 & \beta \end{matrix}\right],\alpha >0$, such that $\det (A)=0$ and $\alpha +\beta =1$. If $I$ denotes $2\times 2$ identity matrix, then the matrix $(I+\mathrm{A}{)}^{8}$ is: [JEE Main 2025, 2 Apr (Shift 1)]

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Let \(\mathrm{A}=\left[\begin{matrix}\alpha & -1 \\ 6 & \beta \end{matrix}\right],\alpha >0\), such that \(\det (A)=0\) …

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