QJEEM24Ma2b9d: JEE Main 2024 Mathematics - Class 12 JEEM24Ma2b9d Solution: Let A be a matrix and . If , then the remainder when is divided …

$\begin{aligned}& |\mathrm{A}|=2 \\& \underbrace{\operatorname{adj}(\operatorname{adj}(\operatorname{adj} \ldots . .(\mathrm{a})))}_{2024 \text { times }}=|\mathrm{A}|^{(\mathrm{n}-1)^{2024}} \\& =|\mathrm{A}|^{2024} \\& =2^{2^{2024}}\end{aligned}$

$\begin{aligned}& 2^{2024}=\left(2^2\right) 2^{2022}=4(8)^{674}=4(9-1)^{674} \\& \Rightarrow 2^{2024} \equiv 4(\bmod 9) \\& \Rightarrow 2^{2024} \equiv 9 \mathrm{~m}+4, \mathrm{~m} \leftarrow \text { even } \\& 2^{9 \mathrm{~m}+4} \equiv 16 \cdot\left(2^3\right)^{3 \mathrm{~m}} \equiv 16(\bmod 9) \\& \quad \equiv 7\end{aligned}$