Is the order of convergence of $\|A\|_\infty$ and the order of $\|A^{-1}\|_\infty$ reciprocal?

Question

For $n\times n$ matrix A, if $\|A\|_\infty=O(1/n)$, can I deduce $\|A^{-1}\|_\infty=O(n)$? Here, $\|A\|_{\infty}=\max _{1 \leq i \leq n} \sum_{j=1}^{n}\left|a_{i j}\right|$.