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JAMB Mathematics 2017 Question 2

Question 2

Matrices and Determinants

If P = [2 1; −3 0] and I is a 2×2 unit matrix, evaluate P2 − 2P + 4I (matrices written row by row, rows separated by ;)

  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, 2 − 2; −6 + 6, −3 − 0 + 4] = [1 0; 0 1].