A) \[{{(-1)}^{n}}{{A}^{-1}}\]
B) \[-{{A}^{-1}}\]
C) \[{{(-1)}^{n-1}}{{A}^{-1}}\]
D) none of these
Correct Answer: B
Solution :
[b] \[{{(-A)}^{-1}}=\frac{adj(-A)}{\left| -A \right|}=\frac{{{(-1)}^{n-1}}adj(A)}{{{(-1)}^{n}}\left| A \right|}\] \[=\frac{adj(A)}{-\left| A \right|}=-{{A}^{-1}}\]
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