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If A = open square brackets table row 1 2 row cell negative 1 end cell 2 end table close square brackets and B =open square brackets table row 3 4 row 2 cell negative 2 end cell end table close square brackets , then (AB)T is-

  1. open square brackets table row 11 cell negative 2 end cell row 5 cell negative 6 end cell end table close square brackets    
  2. open square brackets table row 11 5 row cell negative 2 end cell cell negative 6 end cell end table close square brackets    
  3. open square brackets table row 7 1 row 0 cell negative 8 end cell end table close square brackets    
  4. open square brackets table row 7 0 row 1 cell negative 8 end cell end table close square brackets 

The correct answer is: open square brackets table row 7 1 row 0 cell negative 8 end cell end table close square brackets


    To find the value of open parentheses A B close parentheses to the power of T.
    Given,  A = open square brackets table row 1 2 row cell negative 1 end cell 2 end table close square brackets and B =open square brackets table row 3 4 row 2 cell negative 2 end cell end table close square brackets.
    (AB) = A x B =  open square brackets table row 1 2 row cell negative 1 end cell 2 end table close square brackets x open square brackets table row 3 4 row 2 cell negative 2 end cell end table close square brackets
    (AB) = open square brackets table row 7 0 row 1 cell negative 8 end cell end table close square brackets .
    open parentheses A B close parentheses to the power of T = open square brackets table row 7 1 row 0 cell negative 8 end cell end table close square brackets

    Therefore, by matrix multiplication, open parentheses A B close parentheses to the power of T = open square brackets table row 7 1 row 0 cell negative 8 end cell end table close square brackets.

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