NVAMediumJEE Main 2025 · 4 April, Shift 1Algebra of Matrices

Mathematics Question from JEE Main 2025 · 4 April, Shift 1

Let A=[cosθ0sinθ010sinθ0cosθ]A = \begin{bmatrix} \cos \theta & 0 & -\sin \theta\\ 0 & 1 & 0\\ \sin \theta & 0 & \cos \theta \end{bmatrix}. If for some θ(0,π)\theta \in (0, \pi), A2=ATA^2 = A^T, then the sum of the diagonal elements of the matrix ((A+I)3+(AI)36A)((A + I)^3 + (A - I)^3 - 6A) is equal to _____.

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