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Question

If A =open square brackets table row 0 cell negative i end cell row i 0 end table close square brackets, B =open square brackets table row 0 1 row 1 0 end table close square brackets, C =open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets, then which of the following statement is true-

  1. AB = BA    
  2. AB = – BA    
  3. A2 = BC    
  4. A2 = B + C    

The correct answer is: AB = – BA


    To find the correct statement in the given options.
    Given, A =open square brackets table row 0 cell negative i end cell row i 0 end table close square brackets, B =open square brackets table row 0 1 row 1 0 end table close square brackets, C =open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets.
    AB = open square brackets table row 0 cell negative i end cell row i 0 end table close square brackets x open square brackets table row 0 1 row 1 0 end table close square brackets = open square brackets table row cell negative i end cell 0 row 0 i end table close square brackets
    BA = open square brackets table row 0 1 row 1 0 end table close square brackets x open square brackets table row 0 cell negative i end cell row i 0 end table close square brackets = open square brackets table row i 0 row 0 cell negative i end cell end table close square brackets = -AB

    Therefore, AB = - BA.

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