Linear Algebra
Advanced

Inverse of a 2×2 Matrix

Inverse of a 2×2 matrix (ad−bc ≠ 0).

Formula

A−1=1ad−bc(d−b−ca)A^{-1} = \frac{1}{ad-bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}

Variables

a, b, c, dMatrix entries

Example

Inverse of [[1,2],[3,4]] = (1/−2)[[4,−2],[−3,1]] = [[−2,1],[1.5,−0.5]].

Did You Know?

Matrix inversion is the linear-algebra version of division — and impossible when the determinant is zero.

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