Determinants Matrices Question 73
Question: Consider the following statements:
- If det $ A=0, $ then det $ (adjA)=0 $
- If A is non- singular, then $ \det ({A^{-1}})={{(\det A)}^{-1}} $
Options:
A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] We know that, adj A and A has same value of determinant, if det A = 0, then det (adj A) = 0 So, statement (1) is correct. Also if A is a matrix the determinant of $ {A^{-1}} $ equals inverse of determinant A, so, det $ ({A^{-1}}) $
$ ={{(detA)}^{-1}} $ , if A is non-singular; statement 2 is correct. Thus both (1) and (2) are correct.
BETA
