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5.3 Determinants and Cramer’s Rule - University of Utah
www.math.utah.eduof integers ˙ 1, ..., ˙ ninto natural order 1, ..., n. A consequence of (9) is the relation det(A) = det(AT) where AT means the transpose of A, obtained by swapping rows and columns. This re-lation implies that all determinant theory results for rows also apply to columns. Formula (9) reproduces the de nition for 3 3 matrices given in ...