Determinants Matrices Question 34
Question: If A is a square matrix of order n, then adj (adj A) is equal to
Options:
A) $ |A{{|}^{n-1}}A $
B) $ |A{{|}^{n}}A $
C) $ |A{{|}^{n-2}}A $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] For any square matrix X, we have $ X(adjX)=| X |I _{n} $ Taking X = adj A, we get $ (adjA)[adj(adjA)]=| adjA |I _{n} $
$ \Rightarrow (adjA)[adj(adjA)]={{| A |}^{n-1}}I _{n} $
$ [\because | adjA |={{| A |}^{n-1}}] $
$ \Rightarrow (AadjA)[adj(adjA)]={{| A |}^{n-1}}A $
$ [\because AI _{n}=A] $
$ (| A |I _{n})(adj(adjA))={{| A |}^{n-1}}A $
$ \Rightarrow adj(adjA)={{| A |}^{n-2}}A $
BETA
