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Leibniz formula for determinants
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Everything about Leibniz Formula For Determinants totally explained

In algebra, the Leibniz formula expresses the determinant of a square matrix in terms of permutations of the matrix' elements. Named in honor of Gottfried Leibniz, the formula is » det(A) = sum_ as F(I) is required to be equal to 1.
   Hence the determinant can be defined as the only function » det : mathfrak M_n (mathbb K) longrightarrow mathbb K

which is alternate multilinear w.r.t. columns and such that det(I) = 1.
   

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