imo class 12 determinants

If A is an orthogonal matrix, what is the possible value of |A|?

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If A is an orthogonal matrix, what is the possible value of |A|?

  • A. 0
  • B. ±1
  • C. ±2
  • D. Any real number

Answer: B) ±1

Explanation: For an orthogonal matrix, A Aᵀ = I. Taking determinants, |A||Aᵀ| = |I| => |A|² = 1. So |A| = ±1.

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