Question

If $A$ is an orthogonal matrix , then value of $|A|$ is equal to

• A. $\pm 3$
• B. $\pm 4$
• C. $\pm 2$
• D. $\pm 1$

Answer 1

The correct option is D $\pm 1$

Given that matrix $A$ is orthogonal matrix

Orthogonal matrix is a square matrix with real entities whose columns and rows are orthogonal unit vectors

$\Rightarrow A{A}^T=I$

Apply det on both sides , we get $|A|\times |A^T|=|I|$

$\Rightarrow |A{|}^2=1$

$\Rightarrow |A|=\pm 1$

Therefore the correct option is $D$