Let T:V → W　be a linear transformation, where V and W are finite-dimentional inner product spaces with inner products <・,・>1 and <・,・>2, respectively. prove the following results.

(a) there is a unique adjoint T^* of T, and T^* is linear
(b) if β and γ are orthonormal bases for V and W, respectively, then [T^*] = ([T] )^*
(c) rank(T^*) = rank(T)
(d) <T^*(x),y>1, = <x,T(y)>2 for all x ∈ W and y ∈ V.
(e) For all x ∈ V, T^*T(x) = 0 if and only if T(x)=0.

T:V → V の時は分かったのですが、T:V → W　の時はどう始めたらいいのでしょうか？
宜しくお願いします｡