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Question

If A = open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets and (aI2 + bA)2 = A, then-

  1. a = b =square root of 2    
  2. a = b = 1/square root of 2    
  3. a = b =square root of 3    
  4. a = b = 1/square root of 3    

The correct answer is: a = b = 1/square root of 2


    In the question we were given to find the value of a and b by considering some conditions
    A squared equals open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets equals open square brackets table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close square brackets equals negative I

left parenthesis a I plus b A right parenthesis squared equals left parenthesis a I plus b A right parenthesis left parenthesis a I plus b A right parenthesis
a squared I squared plus a b I A plus b a A I plus b squared A squared
a squared I plus 2 a b A plus b squared A squared
a squared I plus 2 a b A minus b squared I
left parenthesis a squared minus b squared right parenthesis I plus 2 a b A
open square brackets table row cell a squared minus b squared end cell 0 row 0 cell a squared minus b squared end cell end table close square brackets plus 2 a b open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets
equals greater than open square brackets table row cell a squared minus b squared end cell cell 2 a b end cell row cell negative 2 a b end cell cell a squared minus b squared end cell end table close square brackets
B y space s o l v i n g space w e space g e t space
a equals b equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction

    Hence Choice 2 is correct

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