Question

If $A$ is an orthogonal matrix, then

• A. $|A|=0$
• B. $|A|=\pm 1$
• C. $|A|=\pm 2$
• D. None of these

Answer 1

The correct option is B $|A|=\pm 1$

Since, A is an orthogonal matrix
$A{A}^{\prime }=A^{\prime }A=I$
or $A{A}^{\prime }=I$
$\Rightarrow |A{A}^{\prime }|=|I|$
$\Rightarrow |A^{\prime }||A|=1$
$\Rightarrow |A{|}^2=1\because |A|=|A^{\prime }|$
$\Rightarrow |A|=\pm 1$