Any help with this question would be greatly appreciated
Let u be a unit vector and define Qu = I - 2uuT (the T means transpose)
Show that Qu is symmetric and orthogonal, furthermore show that
(Qu)^2 = I
There is no analytic trickery here. For symmetry, just show (I - 2uu^T)^T = (I - 2uu^T) by performing the operations (recall (AB)^T = B^T A^T). Likewise show (I - 2uu^T)(I - 2uu^T) = I. Those imply orthogonality, which is Q^T Q = Q Q^T = I.