Let $A$ be an $n$-by-$n$ matrix with integer entries whose absolute values are bounded by a constant $C$. It is well-known that the entries of the inverse $A^{-1}$ can grow exponentially on $n$. (See the replies to <https://math.stackexchange.com/questions/1146929/estimations-for-the-size-of-the-biggest-entry-in-an-inverse-matrix> .) Can they grow more rapidly than exponentially? Or are they bounded by $(C+O(1))^n$?



Bounding entries of the inverse of a matrix with bounded entries
Christian Remling's answer to this question: [Smallest non-zero eigenvalue of a (0,1) matrix](https://mathoverflow.net/questions/157472/smallest-non-zero-eigenvalue-of-a-0-1-matrix) indicates that the answer is that the entry can grow super-exponentially.


