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Determinants axiomatically
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Definition of multilinear function
The determinant function exists.
The determinant function is unique.
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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A matrix with two equal rows/columns has determinant 0
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Determinants axiomatically