Home/Algebra/Determinants and inverses/Determinant of a product17. Determinants and inversesDeterminant of a productLevel: intermedioIn 17. Determinants and inversesFormulaCopy LaTeXdet(AB)=det(A)det(B)\det(AB)=\det(A)\det(B)det(AB)=det(A)det(B)Tagsalgebradeterminantsdeterminants inversealgebra formulalinearDetailThe overall scaling factor multiplies under composition.Explore the ideaFound an error? Contact us.Related formulasRelatedMatrix product(AB)ij=∑kaikbkj(AB)_{ij}=\sum_k a_{ik}b_{kj}(AB)ij=k∑aikbkjOpen formulaOpen in sectionRelatedInvertibility criterionA invertible ⟺ det(A)≠0A\text{ invertible}\iff\det(A)\ne0A invertible⟺det(A)=0Open formulaOpen in section