Determinants Matrices Question 172
Question: If both $ A-\frac{1}{2}I $ and $ A+\frac{1}{2}I $ are orthogonal matrices, then
Options:
A) A is orthogonal
B) A is skew-symmetric of even order
C) $ A^{2}=\frac{3}{4}I $
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ ( A’-\frac{1}{2}I )( A-\frac{1}{2}I )=I $ and $ ( A’+\frac{1}{2}I )( A+\frac{1}{2}I )=I $
$ \Rightarrow A+A’=0 $
(Subtracting the two results) or $ A’=-A $
$ \Rightarrow A^{2}=-\frac{3}{4}I $ Or $ {{( \frac{-3}{4} )}^{^{n}}}={{(det(A))}^{2}} $ Hence, n is even.
BETA
