Matrix Inverse

Author

Eric W. Weisstein
January 24, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/MatrixInverse.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MatrixInverse.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Explicit Examples

2×2

a2=(({{a, b}, {c, d}}));

Inverse[a2]//TraditionalForm

3×3

a3=Array[a,{3,3}];

Numerator[Inverse[a3]/.a[l__]:>Subscript[a,l]]//TraditionalForm

Det[a3]/.a[l__]:>Subscript[a,l]//TraditionalForm

Inverse[a3]-(1/(Det[a3]))(({{Det[(({{a[2,2], a[2,3]}, {a[3,2], a[3,3]}}))], Det[(({{a[1,3], a[1,2]}, {a[3,3], a[3,2]}}))], Det[(({{a[1,2], a[1,3]}, {a[2,2], a[2,3]}}))]}, {Det[(({{a[2,3], a[2,1]}, {a[3,3], a[3,1]}}))], Det[(({{a[1,1], a[1,3]}, {a[3,1], a[3,3]}}))], Det[(({{a[1,3], a[1,1]}, {a[2,3], a[2,1]}}))]}, {Det[(({{a[2,1], a[2,2]}, {a[3,1], a[3,2]}}))], Det[(({{a[1,2], a[1,1]}, {a[3,2], a[3,1]}}))], Det[(({{a[1,1], a[1,2]}, {a[2,1], a[2,2]}}))]}}))