This post explains an easy and efficient way to implement the inverse of a 3x3 matrix. It’s based on vector operations like previous posts.
Given a 3x3 matrix:
We construct the following three vectors, one for each row of the matrix:
The inverse of the matrix is:
The expression is the determinant of like explained in a previous post. If the determinant is zero, then the matrix has no inverse. Note that the expression appears two times, so it only needs to be calculated once.