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NDA 2 2024 Maths, question 20

Topic: Matrices and determinants

Q20

If PP is a skew-symmetric matrix of order 33, then what is det(P)\text{det}(P) equal to?

  1. (a) −1-1
  2. (b) 00Correct answer
  3. (c) 11
  4. (d) 33

Solution.

Answer: (b) 00

  1. For a skew-symmetric matrix Pᵀ=−P.
  2. Taking determinants in order 3 gives det P=det Pᵀ=det(−P)=−det P.
  3. Hence 2det P=0, so det P=0.