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JAMB Mathematics 2002 Question 16

Question 16

Matrices and Determinants

If P = [2, 1; −3, 0] and I is a 2 × 2 unit matrix, evaluate P2 − 2P + 4I

  1. A.[9, 4; −12, 1]
  2. B.[−3, 0; 0, −3]
  3. C.[1, 0; 0, 1]
  4. D.[1, 4; 4, 1]
Show the answer and explanation

Answer: C ([1, 0; 0, 1])

Explanation

P2 = [1, 2; −6, −3] and 2P = [4, 2; −6, 0]. So P2 − 2P + 4I = [1 − 4 + 4, 0; 0, −3 + 4] = [1, 0; 0, 1].