Assume that h is a linear transformation of V and that (1, . . . , n) is a basis of V. Prove each statement.
(a) If h(i) =  for each basis vector then h is the zero map.
(b) If h(i) = i for each basis vector then h is the identity map.
(c) If there is a scalar r such that h(i) = r ∙ i for each basis vector then h() = r ∙  for all vectors in V.