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If A is a 3×3 matrix with det(A) = 5, then det(2A) is
A5
B10
C40
D125
Answer & Solution
Correct answer: C. 40
1. For an n × n matrix, det(kA) = kⁿ × det(A).
2. Here n = 3, k = 2, det(A) = 5.
3. det(2A) = 2³ × 5 = 8 × 5 = 40.
4. Hence (C) is correct.
_Source: Maharashtra Balbharati Std XII Mathematics & Statistics (Commerce), Ch 1 "Matrices", §1.3 ¶§1.3_
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