Let $A$ be a square uniform matrix with elements in $[0,k]$ over $\mathbb{Z}_q$, $q$ is prime and $k$ is a positive integer less than $q$. If $k=q-1$, then we know the exact probability of $A$ being invertible over $\mathbb{Z}_q$. Is there any method to find the exact probability of $A$ being invertible over $\mathbb{Z}_q$ when $k<<q$?
2026-03-29 15:59:58.1774799998
Inverse of a matrix with small elements
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