Inverse
Inverse[m]
gives the inverse of a square matrix m.
Details and Options

- Inverse works on both symbolic and numerical matrices.
- For matrices with approximate real or complex numbers, the inverse is generated to the maximum possible precision given the input. A warning is given for ill‐conditioned matrices.
- Inverse[m,Modulus->n] evaluates the inverse modulo n.
- Inverse[m,ZeroTest->test] evaluates test[m[[i,j]]] to determine whether matrix elements are zero. The default setting is ZeroTest->Automatic.
- A Method option can also be given. Settings for exact and symbolic matrices include "CofactorExpansion", "DivisionFreeRowReduction", and "OneStepRowReduction". The default setting of Automatic switches among these methods depending on the matrix given.
Examples
open allclose allBasic Examples (3)
Scope (10)
Basic Uses (6)
Special Matrices (4)
The inverse of a sparse matrix is returned as a normal matrix:
When possible, the inverse of a structured matrix is returned as another structured matrix:
IdentityMatrix is its own inverse:
Inverse of HilbertMatrix:
Applications (3)
Properties & Relations (1)
Wolfram Research (1988), Inverse, Wolfram Language function, https://reference.wolfram.com/language/ref/Inverse.html (updated 1996).
Text
Wolfram Research (1988), Inverse, Wolfram Language function, https://reference.wolfram.com/language/ref/Inverse.html (updated 1996).
BibTeX
BibLaTeX
CMS
Wolfram Language. 1988. "Inverse." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Inverse.html.
APA
Wolfram Language. (1988). Inverse. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Inverse.html