Question

If A and B be orthogonal matrices of same size, then

• A. \(|A| = \pm 1\)
• B. \(A^T = -A^{-1}\)
• C. \(|A| = 0\)
• D. AB is not orthogonal

Hint:

The determinant of any orthogonal matrix is always \( \pm 1 \).
- If \( \det(A) = 1 \), the transformation is a pure rotation.
- If \( \det(A) = -1 \), the transformation involves a reflection.

Answer 1

The Correct Option is A