Note Set 18a: Determinants from the ground up

We build up determinants from three basic properties concerned with the volume of the parallelepiped generated by the rows (or columns) of a square matrix. The properties are: (1) The determinant of the identity matrix is 1, (2) swapping two (distinct) rows flips the sign of the determinant, and (3) determinants are multilinear in the rows. All is coming.
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