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Maths-

General

Easy

Question

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 -

Involutary matrix
Idempotent matrix
Orthogonal matrix
Nilpotent matrix

The correct answer is: Orthogonal matrix

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

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