Hva er det(AB)\det(\mathbf{AB})det(AB) for to n×nn\times nn×n-matriser?
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det(AB)=det(A)⋅det(B)\det(\mathbf{AB}) = \det(\mathbf{A})\cdot\det(\mathbf{B})det(AB)=det(A)⋅det(B). Følger: det(A−1)=1/det(A)\det(\mathbf{A}^{-1}) = 1/\det(\mathbf{A})det(A−1)=1/det(A), og det(An)=(det(A))n\det(\mathbf{A}^n) = (\det(\mathbf{A}))^ndet(An)=(det(A))n.
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