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

Answer: (B)

|A|= $\pm$ 1

Answer 2

$AA' = I$

$\therefore|AA'||I|$

⇒ $|A||A| = 1$

$\left\lbrack |A'| = |A|foranysquarematrix \right\rbrack$

∴ $|A| = \pm 1$