Home/Algebra/Determinants and inverses/Cramer's rule17. Determinants and inversesCramer's ruleLevel: intermedioIn 17. Determinants and inversesFormulaCopy LaTeXxi=det(Ai)det(A)x_i=\frac{\det(A_i)}{\det(A)}xi=det(A)det(Ai)Tagsalgebradeterminantsdeterminants inversealgebra formulalinearDetailSolves nonsingular square systems using determinants.Explore the ideaFound an error? Contact us.Related formulasRelated2×2 linear system{a1x+b1y=c1a2x+b2y=c2\begin{cases}a_1x+b_1y=c_1\\a_2x+b_2y=c_2\end{cases}{a1x+b1y=c1a2x+b2y=c2Open formulaOpen in sectionRelatedInverse 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 section