This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Inverse

 Inverse[m]gives the inverse of a square matrix m.
• 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, ZeroTest->test] evaluates to determine whether matrix elements are zero. The default setting is ZeroTest.
• A Method option can also be given. Settings for exact and symbolic matrices include , , and . The default setting of Automatic switches among these methods depending on the matrix given.
Inverse of a 2×2 matrix:
Enter the matrix in a grid:
Inverse of a symbolic matrix:
Inverse of a 2×2 matrix:
 Out[1]=

Enter the matrix in a grid:
 Out[1]=

Inverse of a symbolic matrix:
 Out[1]=
 Applications   (3)
Exact inverse of a Hilbert matrix:
Plot the imaginary parts of a Vandermonde matrix for a discrete Fourier transform:
Plot the inverse of a matrix, shading according to absolute value:
Show positive entries as black and others as white:
The inverse may not exist:
Typically a pseudo inverse does:
Full inverses do not exist for rectangular matrices:
Accurate inverses cannot be found for ill-conditioned machine-precision numerical matrices:
Exact result:
Arbitrary-precision result: