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Q. If $ A $ is an orthogonal matrix, then

ManipalManipal 2010

Solution:

Since, $A$ is an orthogonal matrix, therefore,
$A A'=I \Rightarrow |A \cdot A'|=|I|$
$\Rightarrow |A| \cdot |A'|=1$
$\Rightarrow |A| \cdot| A|=1(\because |I|=1)$
$\Rightarrow |A|^{2}=1(\because |A'|=|A|)$
$\Rightarrow |A|=\pm 1$