MathForces: Math Olympiads
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Author: mathforces
Problem has been solved: 5 times

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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 $X \mod{1009}$.

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