If P = 1 & α & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 is the adjoint of a 3 × 3 matrix A and |A| = 4 , then α is equal to: - Mathematics MCQ JEE Main 2026 | ExamTest.live

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If P = 112 α 34 334 is the adjoint of a 3 \times 3 matrix A and ∣ A ∣ = 4, then α is equal to:

Solution & Step-by-step Explanation

We know that ∣ adj A ∣ = ∣ A ∣^{n - 1} . For a 3 \times 3 matrix, ∣ adj A ∣ = ∣ A ∣^{2} .Given ∣ A ∣ = 4, so ∣ adj A ∣ = 16 . ∣ P ∣ = 1 (12 - 12) - α (4 - 6) + 3 (4 - 6) = 16 . 0 + 2 α - 6 = 16 . 2 α = 22 \Rightarrow α = 11 .

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If P = 112 α 34 334 is the adjoint of a 3 \times 3 matrix A and ∣ A ∣ = 4, then α is equal to:

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