Source: http://www.math.columbia.edu/~bayer/LinearAlgebra/pdf/inverse.pdf

Backup copy (In case of broken link): 3×3 Matrix Inverse

This is an excellent method for finding the inverse of a 3×3 matrix, probably the fastest and easiest method for 3×3.

(Row reduction is better for 4×4 matrices and above.)

This method was first introduced to me by my student!

Featured book:

Linear Algebra and Its Applications, 4th Edition