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JAMB Mathematics 2015 Question 37

Question 37

Matrices and Determinants

Find the matrix T if ST = I where S = (−1 1 / 1 −2) and I is the identity matrix.
(S has rows −1, 1 and 1, −2; each option lists the rows of T)

  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 = S−1. det S = (−1)(−2) − (1)(1) = 1. Swap the leading diagonal and change the signs of the other two entries: T = (−2 −1 / −1 −1). Check: ST gives the identity matrix.