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JAMB Mathematics 2000 Question 15

Question 15

Matrices and Determinants

A matrix P = [a, b; c, d] is such that PT = −P, where PT is the transpose of P. If b = 1, then P is

  1. A.[0, 1; 1, 0]
  2. B.[0, 1; −1, 0]
  3. C.[0, 1; −1, 1]
  4. D.[1, 1; −1, 0]
Show the answer and explanation

Answer: B ([0, 1; −1, 0])

Explanation

PT = [a, c; b, d] must equal [−a, −b; −c, −d]. So a = −a and d = −d give a = d = 0, and c = −b = −1. Hence P = [0, 1; −1, 0].