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General
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Question

If A & B are two square matrices such that B = A–1BA, then (A + B)2 equals-

  1. 0    
  2. A2 + B2    
  3. A2 + 2AB+ B2    
  4. A + B    

The correct answer is: A2 + B2


    As B = –A–1BA
    rightwards double arrow AB = –BA rightwards double arrow AB + BA = 0
    Now, (A + B)2 = A2 + BA+ AB + B2
    = A2 + B2

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