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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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