Simple 3x3 matrix inverse code (C++)

Question

What's the easiest way to compute a 3x3 matrix inverse?

I'm just looking for a short code snippet that'll do the trick for non-singular matrices, possibly using Cramer's rule. It doesn't need to be highly optimized. I'd prefer simplicity over speed. I'd rather not link in additional libraries.

Answer 1

Here's a version of batty's answer, but this computes the correct inverse. batty's version computes the transpose of the inverse.

// computes the inverse of a matrix m
double det = m(0, 0) * (m(1, 1) * m(2, 2) - m(2, 1) * m(1, 2)) -
             m(0, 1) * (m(1, 0) * m(2, 2) - m(1, 2) * m(2, 0)) +
             m(0, 2) * (m(1, 0) * m(2, 1) - m(1, 1) * m(2, 0));

double invdet = 1 / det;

Matrix33d minv; // inverse of matrix m
minv(0, 0) = (m(1, 1) * m(2, 2) - m(2, 1) * m(1, 2)) * invdet;
minv(0, 1) = (m(0, 2) * m(2, 1) - m(0, 1) * m(2, 2)) * invdet;
minv(0, 2) = (m(0, 1) * m(1, 2) - m(0, 2) * m(1, 1)) * invdet;
minv(1, 0) = (m(1, 2) * m(2, 0) - m(1, 0) * m(2, 2)) * invdet;
minv(1, 1) = (m(0, 0) * m(2, 2) - m(0, 2) * m(2, 0)) * invdet;
minv(1, 2) = (m(1, 0) * m(0, 2) - m(0, 0) * m(1, 2)) * invdet;
minv(2, 0) = (m(1, 0) * m(2, 1) - m(2, 0) * m(1, 1)) * invdet;
minv(2, 1) = (m(2, 0) * m(0, 1) - m(0, 0) * m(2, 1)) * invdet;
minv(2, 2) = (m(0, 0) * m(1, 1) - m(1, 0) * m(0, 1)) * invdet;