Determinants Matrices Question 98
Question: $ {{(-A)}^{-1}} $ is always equal to (where A is nth-order square matrix)
Options:
A) $ {{(-1)}^{n}}{A^{-1}} $
B) $ -{A^{-1}} $
C) $ {{(-1)}^{n-1}}{A^{-1}} $
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ {{(-A)}^{-1}}=\frac{adj(-A)}{| -A |}=\frac{{{(-1)}^{n-1}}adj(A)}{{{(-1)}^{n}}| A |} $
$ =\frac{adj(A)}{-| A |}=-{A^{-1}} $
BETA
