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Mathematics · 2025

JEE Main · 4 April 2025, Shift 1 · Q22

Let A= [cos θ, 0, - sin θ; 0, 1, 0; sin θ, 0, cos θ]. If for some θ ∈(0, π), A^2=A^T, then the sum of the diagonal elements of the matrix ( A + I…

Let $\displaystyle A=\left[\begin{array}{ccc}\cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta\end{array}\right]$. If for some $\displaystyle \theta \in(0, \pi), A^2=A^T$, then the sum of the diagonal elements of the matrix $\displaystyle (\mathrm{A}+\mathrm{I})^3+(\mathrm{A}-\mathrm{I})^3-6 \mathrm{~A}$ is equal to $\displaystyle \_\_\_\_$.
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JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.