If A is an invertible matrix, then what is det ( A − 1 ) equal to?, det A, det A 1 , 1, None of the above

If A is an invertible matrix, then what is det ( A − 1 ) equal to?

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If $A$ is an invertible matrix, then what is det $\left(A^{-1}\right)$ equal to?

MathematicsDeterminantsNDANDA 2014 (Phase 2)

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Solution:

1385 Upvotes Verified Answer

The correct answer is: $\frac{1}{\operatorname{det} A}$

$\operatorname{det}\left(\mathrm{A}^{-1}\right)=\frac{1}{\operatorname{det} \mathrm{A}}$

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