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Let F(alpha) =open square brackets table row cell cos invisible function application alpha end cell cell negative sin invisible function application alpha end cell 0 row cell sin invisible function application alpha end cell cell cos invisible function application alpha end cell 0 row 0 0 1 end table close square brackets, where alpha  element of R. Then (F(alpha))–1 is equal to

  1. F (–alpha)    
  2. F (alpha –1)    
  3. F (2alpha)    
  4. none of these    

The correct answer is: F (–alpha)


    We are asked to find the value of [F(α)] inverse
    F left parenthesis alpha right parenthesis F left parenthesis negative alpha right parenthesis space equals open square brackets table row cell cos alpha end cell cell negative sin alpha end cell 0 row cell sin alpha end cell cell cos alpha end cell 0 row 0 0 1 end table close square brackets open square brackets table row cell cos alpha end cell cell sin alpha end cell 0 row cell negative sin alpha end cell cell cos alpha end cell 0 row 0 0 1 end table close square brackets
F left parenthesis alpha right parenthesis F left parenthesis negative alpha right parenthesis space equals open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets equals I
F left parenthesis negative alpha right parenthesis space equals space left square bracket F left parenthesis alpha right parenthesis right square bracket to the power of negative 1 end exponent

    Therefore the correct option is choice 1

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