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JEE Main 2024 Mathematics question

MathematicsMatricesJEE Main 2024

Let A and B be two square matrices of order 3 such that |A| = 3 and |B| = 2. Then |Aᵀ A (adj(2A))⁻¹ (adj(4B)) (adj(AB))⁻¹ A Aᵀ| is equal to:

Answer: (A)

Solution

|adj M| = |M|² for order 3: |adj(2A)| = (8·3)² = 576, |adj(4B)| = (64·2)² = 16384,

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Question ID VK-011558