Q:

Simple 3x3 matrix inverse code (C++)

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.

A:

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;

A:

Why don't you try to code it yourself? Take it as a challenge. :)
For a 3×3 matrix

(source: wolfram.com) 
the matrix inverse is

(source: wolfram.com) 
I'm assuming you know what the determinant of a matrix |A| is.

Images (c) Wolfram|Alpha and
  mathworld.wolfram (06-11-09,
  22.06)

A:

This piece of code computes the transposed inverse of the matrix A:

double determinant =    +A(0,0)*(A(1,1)*A(2,2)-A(2,1)*A(1,2))
                        -A(0,1)*(A(1,0)*A(2,2)-A(1,2)*A(2,0))
                        +A(0,2)*(A(1,0)*A(2,1)-A(1,1)*A(2,0));
double invdet = 1/determinant;
result(0,0) =  (A(1,1)*A(2,2)-A(2,1)*A(1,2))*invdet;
result(1,0) = -(A(0,1)*A(2,2)-A(0,2)*A(2,1))*invdet;
result(2,0) =  (A(0,1)*A(1,2)-A(0,2)*A(1,1))*invdet;
result(0,1) = -(A(1,0)*A(2,2)-A(1,2)*A(2,0))*invdet;
result(1,1) =  (A(0,0)*A(2,2)-A(0,2)*A(2,0))*invdet;
result(2,1) = -(A(0,0)*A(1,2)-A(1,0)*A(0,2))*invdet;
result(0,2) =  (A(1,0)*A(2,1)-A(2,0)*A(1,1))*invdet;
result(1,2) = -(A(0,0)*A(2,1)-A(2,0)*A(0,1))*invdet;
result(2,2) =  (A(0,0)*A(1,1)-A(1,0)*A(0,1))*invdet;

Though the question stipulated non-singular matrices, you might still want to check if determinant equals zero (or very near zero) and flag it in some way to be safe.

