For (A): write both vectors as lin. comb. of the given orthonormal basis: , so:
, as .
OTOH, , and summing over i from 1 to n we get the same as above.
Wat you did is wrong because one step before the last you write there the product of and etc...what's this??
About (B) also I don't understand what's going on: what's , anyway? Though I suspect it is the canonical isomorphism from assigning to every vectors its coordinates wrt the basis ...but then the exercise is pretty straightforward, after you fix the notation's mistakes.