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?

  • $\begingroup$ I have only noticed that if determinant value is +1 or -1 then the situation is true. $\endgroup$
    – user630002
    Dec 29, 2018 at 17:17
  • 2
    $\begingroup$ Cramer's rule${}$? $\endgroup$ Dec 29, 2018 at 17:18
  • $\begingroup$ Can you please elaborate a little bit @Lord Shark The Unknown? $\endgroup$
    – user630002
    Dec 29, 2018 at 17:19
  • $\begingroup$ @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. $\endgroup$
    – user630002
    Dec 29, 2018 at 17:28
  • $\begingroup$ @AkashRoy That's the question, but did you actually read the first answer? $\endgroup$ Dec 29, 2018 at 17:41