imo class 12 determinants

If A is a 3×3 matrix and |A| = 5, what is the value of |3A|?

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#IMO#Class 12#Mathematics#Determinants#mathematical-reasoning

If A is a 3×3 matrix and |A| = 5, what is the value of |3A|?

  • A. 15
  • B. 45
  • C. 135
  • D. 125

Answer: C) 135

Explanation: For an n×n matrix, |kA| = kⁿ|A|. Here n=3, so |3A| = 3³ × 5 = 27 × 5 = 135.

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