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Upper bounds for difference of entries between matrices and their inverses in $\mathsf{GL}_k(\mathbb Z)$
Let $a(M)$ be the maximum absolute value of entries of matrix $M\in\mathsf{GL}_k(\mathbb Z)$.
$M^{-1}\in\mathsf{GL}_k(\mathbb Z)$ holds.
What is a good upper bound for $|a(M)-a(M^{-1})|$?
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