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Determinants axiomatically

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The determinant function is unique.
Definition of multilinear function
The determinant function exists.
A determinant is a multilinear function
Adding a multiple of one row to another row does not change the determinant.
Switching two rows multiplies the determinant by -1.
Multiplying a row by a scalar multiplies the determinant by that scalar.
A matrix with two equal rows/columns has determinant 0
A matrix with a 0 row/column has determinant 0

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The determinant function exists.

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The determinant function is unique.Close match
Determinants axiomaticallyClose match
The permutation expansion for determinantsClose match
Switching two rows multiplies the determinant by -1.Close match
A determinant is a multilinear functionClose match
A matrix and its transpose have the same determinant.Close match
A matrix with two equal rows/columns has determinant 0Close match
A matrix with a 0 row/column has determinant 0Close match
Definition of the determinant in terms of the effect of elementary row operationsClose match
Determinants multiply: det(AB) = det(A)det(B)Close match
DeterminantsClose match
Theorem describing the determinants of elementary matrices.Close match
Adding a multiple of one row to another row does not change the determinant.Close match
Definition of determinant of a matrix as a cofactor expansion across the first rowClose match
The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.Close match
Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.Close match
The determinant of the inverse of A is the reciprocal of the determinant of A.Close match
Multiplying a row by a scalar multiplies the determinant by that scalar.Close match
The determinant of a matrix can be computed as a cofactor expansion across any row.Close match
Definition of multilinear functionRelated

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