Determinants Matrices Question 31
Question: If and if A is invertible, then which of the following is not true-
Options:
A) $ | A |=| B | $
B) $ | A |=-| B | $
C) $ | adjA |=| adjB | $
D) A is invertible if and only if B is invertible
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] (Multiplying $ R_2 $ by -1) (Multiplying $ C_2 $ by -1) (Changing $ R_1 $ with $ R_2 $ )
Hence, $ | A |=-| B |, $ obviously when $ | A |\ne 0,| B |\ne 0. $ Also, $ | adjB |={{| B |}^{2}}={{(-| A |)}^{2}}={{| A |}^{2}}. $
BETA
