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

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Basic Examples  (3)

Inverse of a 2×2 matrix:

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Enter the matrix in a grid:

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Inverse of a symbolic matrix:

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Applications  (3)

Properties & Relations  (1)

Possible Issues  (3)

See Also

PseudoInverse  LinearSolve  RowReduce  NullSpace  LinearSolveFunction  MatrixRank

Tutorials

Introduced in 1988
(1.0)
| Updated in 1996
(3.0)