Bounding $\|A^{-1}\|$ in terms of $\det A$ where $A$ is an integer matrix

Question

Let $d\geq 1$ be an integer. Is there a function $f:\mathbb{N}\rightarrow\mathbb{R}$ (possibly depending on $d$) such that:

1. $f$ tends to $0$ as $n$ approaches $\infty$.
2. For every $d\times d$ matrix $A$ with entries in $\mathbb{Z}$ and a nonzero determinant, we have $\| A^{-1}\|\leq f(|\det(A)|)$.

Notes:

1. $\|\cdot\|$ refers to any norm on $M_d(\mathbb{R})$. The particular chosen norm does not matter in the context of this question.
2. The entries of $A^{-1}$ are usually not integral.