Multiply matrices A * B * C * D * E, where each does the following: A: translate the plane to the origin. B: rotate the plane to the XY plane. C: invert the Z coordinate. D: inverse of matrix B E: inverse of matrix A
where (a, b, c) is the unit vector n, aa = a * a, i.e. ''a'' squared.
This is a 3x3 matrix reflecting in a plane through the origin. Note it is NOT a rotation matrix, so do not try to check it as such. E.g. it''s determinant is not 1 but -1.
If the plane is not through the origin it requires a 4x4 matrix with a translation element. The translation part equals what happens to the origin when reflected, and the origin is reflected though a distance twice it''s distance from the plane along the direction of the plane normal, i.e. just work out the position of the origin after the reflection to complete the matrix.