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Orthogonal Matrix

If A is an ...

Question

If $A$ is an unitary matrix then $| A |$ is equal to:

1

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- 1

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\pm 1

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2

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Solution

The correct option is A $\pm 1$
Since, A is a unitary matrix
$A A^{} = I$
$d e t A \times d e t A^{} = d e t I$
$\Rightarrow (d e t A)^{2} = 1$ ( $∵ | A | = |^{T} |$ )
$\Rightarrow d e t A = \pm 1$

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