Matrix Identity Sum (Jee Mains)

Formation, Types & Operations

Medium

Matrix Identity Sum

Let A = $\left[ {\begin{array}{*{20}{c}} {\cos \theta }&0&{ - \sin \theta }\\[0.9em] 0&1&0\\[0.9em] {\sin \theta }&0&{\cos \theta } \end{array}} \right]$ . If for some θ ∈ (0, π), A² = A^T, then the sum of the diagonal elements of the matrix (A + I)³ + (A – I)³ – 6A is equal to ____.

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