Question

If $A$ is an orthogonal matrix, then

• A. $\det A=$ not exist
• B. $\det A=0$
• C. $\det A=\pm 1$
• D. None of these

Answer 1

Answer: (C)

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