Determinants Matrices Question 147
Question: Let A, B, C, D be (not necessarily square) real matrices such that $ A^{T}=BCD;B^{T}=CDA; $
$ C^{T}=DAB $ and $ D^{T}=ABC $ for the matrix $ S=ABCD,S^{3}= $
Options:
A) I
B) $ S^{2} $
C) S
D) O
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ S=ABCD=A(BCD)=AA^{T}…(1) $
$ S^{3}=(ABCD)(ABCD)(ABCD) $
$ =(ABC)(DAB)(CDA)(BCD) $
$ =D^{T}C^{T}B^{T}A^{T} $
$ ={{(BCD)}^{T}}A^{T}=AA^{T}…(2) $ From (1) and (2), $ S=S^{3} $
BETA
