Determinants Matrices Question 64
Question: Let $ A={{[a _{ij}]} _{m\times m}} $ be a matrix and $ C={{[c _{ij}]} _{m\times m}} $ be another matrix where $ c _{ij} $ is the cofactor of $ a _{ij} $ Then, what is the value of $ |AC| $ -
Options:
A) $ |A|^{m-1} $
B) $ |A|^{m} $
C) $ |A|^{m+1} $
D) Zero
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] Let $ A={{[a _{ij}]} _{m\times m}} $ be a matrix and $ C={{[c _{ij}]} _{m\times m}} $ be another matrix where $ c _{ij} $ is the cofactor of $ a _{ij} $
$ \therefore $ The value of $ | AC |={{| A |}^{m+1}} $
BETA
