Prove that the following inner [scalar] product ...

a) ❮x,y❯ = ❮y,x❯ b) ❮x,y+z❯ = ❮x,y❯ + ❮x,z❯ c) ❮λx,y❯ = λ❮x,y❯ d) ❮x,x❯ ≥ 0, with ❮x,x❯ =0 ❮=❯ x=0 where ❮x,y❯ = ∑xiyi where i=1,..,n