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Question

Let A = $open square brackets table row 0 cell 2 y end cell z row x y cell negative z end cell row x cell negative y end cell z end table close square brackets$ and A'. A = I, then the value of x² + y² + z² is-

1
2
½
None of these

The correct answer is: 1

I = A'A = $open square brackets table row 0 x x row cell 2 y end cell y cell negative y end cell row z cell negative z end cell z end table close square brackets$ $open square brackets table row 0 cell 2 y end cell z row x y cell negative z end cell row x cell negative y end cell z end table close square brackets$
= $open square brackets table row cell 2 x to the power of 2 end exponent end cell 0 0 row 0 cell 6 y to the power of 2 end exponent end cell 0 row 0 0 cell 3 z to the power of 2 end exponent end cell end table close square brackets$
$therefore$ 2x² = 6y² = 3z² = 1
$therefore$ x² + y² + z² = $fraction numerator 1 over denominator 2 end fraction$ + $fraction numerator 1 over denominator 6 end fraction$ + $fraction numerator 1 over denominator 3 end fraction$ = $fraction numerator 3 plus 1 plus 2 over denominator 6 end fraction$ =1

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