I would very much appreciate help with the following question:

(i) Prove that the dot product of any two vectorsu,v∈ Rn isu^{T}v.

(ii) Given a MatrixAand vectorsu,v∈ Rn so thatAu . Av = u . v, prove thatAis orthogonal

(for part (ii)we can assume that (AB)^t= B^t A^t)