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JAMB Mathematics 1999 Question 12

Question 12

Matrices and Determinants

Find the matrix T if ST = I where S = (−1 1 / 1 −2) and I is the identity matrix. (Rows are separated by /.)

  1. A.(−2 1 / −1 1)
  2. B.(−2 −1 / −1 −1)
  3. C.(−1 −1 / 0 −1)
  4. D.(−1 1 / 0 1)
Show the answer and explanation

Answer: B ((−2 −1 / −1 −1))

Explanation

T is the inverse of S. det S = 2 − 1 = 1, so S⁻¹ = (−2 −1 / −1 −1): swap the diagonal entries and change the signs of the others.