Determinants Matrices Question 41
Question: If D is determinant of order 3 and D’ is the determinant obtained by replacing the elements of D by their cofactors, then which one of the following is correct ?
Options:
A) $ D’=D^{2} $
B) $ D’=D^{3} $
C) $ D’=2D^{2} $
D) $ D’=3D^{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] D- = cofactor D
$ \Rightarrow | D’ |=| cofactorD | $
$ \Rightarrow | D’ |={{| D |}^{3-1}} $ .
$ \Rightarrow | D’ |={{| D |}^{2}} $ . So $ D’=D^{2} $ .
BETA
