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Determinants and operations on matrices

Created over 8 years ago, updated 10 days ago

Determinants and matrix operations:

  • $\det(AB) = \det(A)\det(B)$
  • $\det(A^T) = \det(A)$
  • $\det(cA) = c^n \det(A)$ for $n \times n$ matrix
  • $\det(A^{-1}) = 1/\det(A)$
  • Row swap changes sign of determinant
  • Row scaling by $c$ multiplies determinant by $c$
  • Row replacement does not change determinant