Question

$If space straight A equals space open square brackets table row 1 2 row 2 1 end table close square brackets space comma space straight f space left parenthesis straight x right parenthesis space equals straight x to the power of 2 space end exponent minus 2 straight x minus 3 space show space that space straight f left parenthesis straight A right parenthesis equals straight O$

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Solution

Here space straight f space left parenthesis straight x right parenthesis space equals straight x to the power of 2 space end exponent minus 2 straight x minus 3 space show space that space straight f left parenthesis straight A right parenthesis equals straight O therefore space space space space space space straight f space left parenthesis straight A right parenthesis space equals space straight A to the power of 2 space end exponent space minus 2 straight A minus 3 space straight I space space space space space space space space space space space space space straight A space equals space open square brackets table row 1 cell space space 2 end cell row 2 cell space space 1 end cell end table close square brackets space space space space space space space space space space straight A to the power of 2 space end exponent space space equals space open square brackets table row 1 cell space space 2 end cell row 2 cell space space 1 end cell end table close square brackets space space space space open square brackets table row 1 cell space space 2 end cell row 2 cell space space 1 end cell end table close square brackets space space equals space open square brackets table row cell 1 plus 4 end cell cell space space space space 2 plus 2 end cell row cell 2 plus 2 end cell cell space space space 4 plus 1 end cell end table close square brackets space equals space open square brackets table row 5 cell space 4 end cell row cell 4 space end cell cell space 5 end cell end table close square brackets space space space space space space space space space space space space straight f space left parenthesis straight A right parenthesis space equals space space space straight A to the power of 2 space end exponent minus 2 straight A minus 3 space straight I space space space space space space space space space space space space space space space space space equals space open square brackets table row 5 cell space space 4 end cell row 4 cell space space 5 end cell end table close square brackets space minus 2 space space open square brackets table row cell 1 space space end cell cell space 2 end cell row 2 cell space 1 end cell end table close square brackets space space minus 3 space space open square brackets table row 1 cell space space 1 end cell row 0 cell space space space 0 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space equals space open square brackets table row 5 cell space space 4 end cell row 4 cell space space 5 end cell end table close square brackets space space space plus space open square brackets table row cell negative 2 end cell cell negative 4 end cell row cell negative 4 end cell cell negative 2 end cell end table close square brackets space plus space open square brackets table row cell negative 3 end cell 0 row 0 cell negative 3 end cell end table close square brackets space space space space space space space space space space space space space space space space space equals space open square brackets table row cell 5 minus 2 minus 3 end cell cell space space space space 4 minus 4 plus 0 end cell row cell 4 plus 4 minus 0 end cell cell space space space 5 minus 2 minus 3 end cell end table close square brackets space space equals space open square brackets table row 0 cell space space space 0 end cell row 0 cell space space space 0 end cell end table close square brackets space equals space straight O space space space space space

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Matrices

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