I would very much appreciate help with the following question:
(i) Prove that the dot product of any two vectors u,v ∈ Rn is uTv.
(ii) Given a Matrix A and vectors u,v ∈ Rn so that Au . Av = u . v , prove that A is orthogonal
(for part (ii)we can assume that (AB)^t= B^t A^t)