Home/Algebra/Determinants and inverses/2×2 determinant17. Determinants and inverses2×2 determinantLevel: intermedioIn 17. Determinants and inversesFormulaCopy LaTeXdet(abcd)=ad−bc\det\begin{pmatrix}a&b\\c&d\end{pmatrix}=ad-bcdet(acbd)=ad−bcTagsalgebradeterminantsdeterminants inversealgebra formulalinearDetailOriented area scaling factor in 2D.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 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