Question:
If |A| = 2, B = adj(adj(2A)), A is a 3×3 matrix, and tr(A) = 3, what is tr(B) + |B|?
If |A| = 2, B = adj(adj(2A)), A is a 3×3 matrix, and tr(A) = 3, what is tr(B) + |B|?
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The determinant and trace of a matrix can be used to simplify problems involving adjugates and scalar multiples of matrices.
Updated On: Jan 14, 2026
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The Correct Option is B
Solution and Explanation
To solve this, recall the properties of determinants and adjugates. If \( A \) is a 3×3 matrix, then \( |\text{adj}(A)| = |A|^2 \).
Similarly, for the adjugate of a scalar multiple of a matrix, use the identity \( \text{adj}(kA) = k^{n-1} \text{adj}(A) \),
where \( n \) is the order of the matrix.
Solve for \( B \) and then compute the trace and determinant to find the solution.
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