Determinants Matrices Question 117
Question: Let A and B be $ 3\times 3 $ matrices of real numbers, where A is symmetric, B is skew symmetric, and $ (A+B)(A-B)=(A-B)(A+B). $ If $ {{(AB)}^{t}}={{(-1)}^{k}}AB $ where $ {{(AB)}^{t}} $ is the transpose of the matrix AB, then k is
Options:
A) Any integer
B) Odd integer
C) Even integer
D) Cannot say anything
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ (A+B)(A-B)=(A-B)(A+B) $
$ \Rightarrow AB=BA $ as A us symmetric and B is skew-symmetric $ {{(AB)}^{t}}=-AB $
$ \Rightarrow k $ is an odd integer.
BETA
