Question

If the orthogonal square matrix A and B satisfy, det A + det B = 0, then the value of det(A+B) =

• A. Equals 0
• B. Equals 1
• C. Equals -1
• D. Equals 1 or -1, and both these values are of possible single choice

Answer 1

The correct option is A Equals 0

$A{A}^T=I\Rightarrow |A|=\pm 1$
If |A|=1, then |B| =-1
Then |A+B|=0