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QUESTION

Show that if the $n\times n$ matrix $A$ is invertible then
$\det(A^{-1})=(\det A)^{-1}$.

[Hint: consider $AA^{-1}=I$.]

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ANSWER

$\det AB=\det A\times\det B$, so 1=$\det I=\det(AA^{-1})=\det
A\times\det A^{-1}$.



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