Let A and B be orthogonal and det A+det B=0. Then | Mathematics | SolveeIt | Solveeit

Today, August 19

Question

Let A and B be orthogonal and det A+det B=0. Then

A

A+B is singular

B

A+B is non-singular

C

A+B is orthogonal

D

A+B is skew-symmetric

Answer

A+B is singular

Explanation

Solution

The correct answer is option (A): A+B is singular

AAT=I $\Rightarrow$ |A|= $\pm 1$

If |A|=1 then |B|=-1

Then |A+B|=0

So, A+B is singular