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Theorem describing the determinants of elementary matrices.

Created over 8 years ago, updated 10 days ago

Theorem: The determinants of elementary matrices are:

  • Row swap: $\det(E) = -1$
  • Row scaling by $c$: $\det(E) = c$
  • Row replacement: $\det(E) = 1$

These follow from how each operation affects the determinant of the identity matrix.