Home/Algebra/Determinants and inverses/Inverse of a 2×2 matrix17. Determinants and inversesInverse of a 2×2 matrixLevel: intermedioIn 17. Determinants and inversesFormulaCopy LaTeXA−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)Tagsalgebradeterminantsdeterminants inversealgebra formulalinearDetailInverts a nonsingular 2×2 matrix.Explore the ideaFound an error? Contact us.Related formulasRelatedInvertibility criterionA invertible ⟺ det(A)≠0A\text{ invertible}\iff\det(A)\ne0A invertible⟺det(A)=0Open formulaOpen in sectionRelatedMatrix formAx=bA\mathbf x=\mathbf bAx=bOpen formulaOpen in sectionRelatedInverse transformationT−1(y)=A−1yT^{-1}(y)=A^{-1}yT−1(y)=A−1yOpen formulaOpen in section