Determinants Matrices Question 61
Question: If adj $ B=A, $
$ | P |=| Q |=1, $ then adj $ ({Q^{-1}}B{P^{-1}}) $ is
Options:
A) $ PQ $
B) $ QAP $
C) $ PAQ $
D) $ P{A^{-1}}Q $
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] Given $ adjB=A,| P |=| Q |=1 $ Consider, adj $ ({Q^{-1}}B{P^{-1}}) $
$ =(adj{P^{-1}})(adjB)(adj{Q^{-1}}) $
$ ={{(adjP)}^{-1}}A.{{(adjQ)}^{-1}}={{({P^{-1}})}^{-1}}A{{({Q^{-1}})}^{-1}} $
$ =PAQ $ .
BETA
