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If A and B are square matrices of the same order such that A = - B - 1 A B , then A + 3 B 2 is equal to

Options

  1. AA + 3 B
  2. BA 2 + 9 B 2
  3. CA 2 + 6 A B + A B 2
  4. DO

Correct answer

B. A 2 + 9 B 2

Step-by-step solution

A = - B - 1 A B ⇒ B A = - A B ⇒ B A + A B = 0 A + 3 B 2 = A 2 + 9 B 2 + 3 A B + 3 B A = A 2 + 9 B 2

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