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Let A be a 3x3 matrix such that $\det (A) = - 2$ . Then $\det (- 2 A^{- 1})$ is equal to

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-4

-2

answer is A.

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Detailed Solution

As $A^{- 1}$ is a 3x3 matrix,

$\begin{array}{l} \det (- 2 A^{- 1}) = (- 2)^{3} \det (A^{- 1}) \\ = (- 2)^{3} (\det (A))^{- 1} \\ = (- 8) (- \frac{1}{2}) = 4 \end{array}$

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