Home/Algebra/Determinants and inverses/Invertibility criterion17. Determinants and inversesInvertibility criterionLevel: intermedioIn 17. Determinants and inversesFormulaCopy LaTeXA invertible ⟺ det(A)≠0A\text{ invertible}\iff\det(A)\ne0A invertible⟺det(A)=0Tagsalgebradeterminantsdeterminants inversealgebra formulalinearDetailCharacterizes invertible square matrices.Explore the ideaFound an error? Contact us.Related formulasRelatedInverse of a 2×2 matrixA−1=1ad−bc(d−b−ca)A^{-1}=\frac1{ad-bc}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}A−1=ad−bc1(d−c−ba)Open formulaOpen in sectionRelatedLinear independence∑icivi=0⇒c1=⋯=ck=0\sum_i c_iv_i=0\Rightarrow c_1=\cdots=c_k=0i∑civi=0⇒c1=⋯=ck=0Open formulaOpen in section