${(- A)}^{- 1}$ is always equal to (where $A$ is $n t h$ order square matrix)

{(- 1)}^{n} A^{- 1}

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{- A}^{- 1}

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{(- 1)}^{n - 1} A^{- 1}

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none of these

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Solution

The correct option is B ${- A}^{- 1}$
We know that if $A^{- 1}$ exist then $(c A)^{- 1} = \frac{1}{c} A^{- 1}$ where c is a constant
Hence $(- A)^{- 1} = \frac{1}{- 1} A^{- 1} = - A^{- 1}$

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