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Let A = 2 3 5 7 and B = a 0 0 b where a , b ∈ N . The number of matrices B such that A B = B A , is equal to

Options

  1. A0
  2. B1
  3. C2
  4. Dinfinite

Correct answer

D. infinite

Step-by-step solution

A B = 2 3 5 7 a 0 0 b = 2 a 3 b 5 a 7 b B A = a 0 0 b 2 3 5 7 = 2 a 3 a 5 b 7 b ∴ A B = B A ⇒ a = b (infinite matrices are possible)

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