Determinants Matrices Question 31
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 det(A) ≠ 0
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
