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If A = fraction numerator 1 over denominator 9 end fraction open square brackets table row cell negative 8 end cell 1 4 row 4 4 7 row 1 cell negative 8 end cell 4 end table close square brackets then A is -

  1. Involutary matrix    
  2. Idempotent matrix    
  3. Orthogonal matrix    
  4. Nilpotent matrix    

The correct answer is: Orthogonal matrix


    A to the power of T end exponent equals fraction numerator 1 over denominator 9 end fraction open square brackets table row cell negative 8 end cell 4 1 row 1 4 cell negative 8 end cell row 4 7 4 end table close square brackets
    A A to the power of T end exponent equals fraction numerator 1 over denominator 81 end fraction open square brackets table row 81 0 0 row 0 81 0 row 0 0 81 end table close square brackets equals I
    rightwards double arrowA is orthogonal matrix
    Hence (C) is correct.

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