Excerpt from Invariantive Characterizations of Linear Algebras With the Associative Law Not Assumed: A Dissertation Submitted to the Faculty of the Ogden Graduate School of Science in Candidacy for the Degree of Doctor of Philosophy, Department of Mathematics N O analogous theorem exists concerning the interchange of two rows.
Lemma 2; Any hypercomplex determinant two of whose columns are identical is zero.
For by the interchange of the two identical columns the determinant is nu altered, and yet changes in sign.
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