# Bounding entries of the inverse of a matrix with bounded entries

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 $$(C+O(1))^n$$?

• If it would be possibel to add a row and column to a Hadamard (e.g. Walsh matrices)$such that determinant is 1 the entries could grow like$(\sqrt{n}C)^n\$. Mar 25 '19 at 16:08