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JAMB Mathematics 2010 Question 27

Question 27

Matrices and Determinants

If P = (2 −3; 1 1), what is P−1? (Matrices written row by row.)

  1. A.(1/5 3/5; 1/5 2/5)
  2. B.(1/5 3/5; −1/5 2/5)
  3. C.(−1/5 3/5; −1/5 2/5)
  4. D.(−1/5 −3/5; −1/5 −2/5)
Show the answer and explanation

Answer: B ((1/5 3/5; −1/5 2/5))

Explanation

The determinant is 2 + 3 = 5. Swap the diagonal and change the other signs: P−1 = 1/5 (1 3; −1 2) = (1/5 3/5; −1/5 2/5).