Suppose I have a matrix say $A$ with integer elements. I want to have the elements of $A^{-1}$ to be integers . Here $A^{-1}$ stands for inverse matrix of $A$ . How can I prove that this is achievable iff the determinant value of $A$ is unimodular?
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$\begingroup$ I have only noticed that if determinant value is +1 or -1 then the situation is true. $\endgroup$– user630002Dec 29, 2018 at 17:17
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2$\begingroup$ Cramer's rule${}$? $\endgroup$– Angina SengDec 29, 2018 at 17:18
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$\begingroup$ Can you please elaborate a little bit @Lord Shark The Unknown? $\endgroup$– user630002Dec 29, 2018 at 17:19
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$\begingroup$ @Jose I want to prove it for an $n×n$ matrix, the link you have given is only showing the proof for a $2×2$, I guess. $\endgroup$– user630002Dec 29, 2018 at 17:28
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$\begingroup$ @AkashRoy That's the question, but did you actually read the first answer? $\endgroup$– José Carlos SantosDec 29, 2018 at 17:41
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