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Inverse matrix calculator

This online calculator finds inverse matrix via adjugate matrix

The calculator below computes inverse matrix via adjugate matrix. Some theory and formulas can found under the calculator.

PLANETCALC, Inverse of a matrix

Inverse of a matrix

Digits after the decimal point: 2
Inverse of a matrix

The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A^{-1} such that
AA^{-1} = A^{-1}A = I

This calculator uses adjugate matrix to compute matrix inverse like
A^{-1} = \frac{1}{\det A}\cdot C^*

Adjugate matrix is the transpose of the cofactor matrix of A.
{C}^{*}= \begin{pmatrix}  {A}_{11} & {A}_{21} & \cdots & {A}_{n1} \\ {A}_{12} & {A}_{22} & \cdots & {A}_{n2} \\ \vdots & \vdots & \ddots & \vdots \\ {A}_{1n} & {A}_{2n} & \cdots & {A}_{nn} \\ \end{pmatrix}

Cofactor of a_{ij} of A is defined as
where M_{ij} is a minor of a_{ij}.

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