# Mathrix

Author: mathforces
Problem has been solved: 5 times

Русский язык | English Language

Consider an invertible matrix $A$ of size $1000\times 1000$. Let $S_{A}$ be the set of all matrices $A_i$ such that the rows of $A_i$ are a permutation of the rows of $A$. Let $X$ the number of matrices $B\in S_{A}$ such that $\det(A+B) \ne 0$. Find $X \mod{1009}$.