I need to prove this statement: "If $A$ invertible, then exist a permutation of its rows leaving no-zeros on the diagonal" and I tried using the definitos of invertible matrices and $LU$ factorization, but without results.
Can you help me, please?
2026-04-12 04:45:06.1775969106
If matrix $A$ is invertible, then there is a permutation of its rows leaving no-zeros on the diagonal
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Consider the full expansion of the determinant. If it is nonzero, then at least one of its terms must be.