This is the same problem as the rotation about an axis. What you need is a matrix (any matrix) that satisfies the following corner constraint: one axis must point toward $(-2, 2, 0)$ in the case of a rotation this matrix must be a rotation matrix, in the case of a planar mirror it just has to span the 3D space. But since we know how to make a an arbitrary rotation matrix we use same approach.
- Pick any vector(u) thats not paralell to normal (n)
- take cross product of u and n for b
- take cross product of n and b for a
you now have now an arbitrary rotation matrix with one axis defined using vectors n, b and a. Otherwise same as the last question.