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Prove that if $A$ is a square matrix with integer entries and $\det(A)=\pm 1$, then the inverse of $A$ contains all integer entries.

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What do you know? What have you tried? –  Julian Kuelshammer Oct 14 '12 at 11:07

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up vote 3 down vote accepted

Hint: Consider the inverse written in terms of the adjugate matrix.

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