Verify that each of the following is an isomorphism (Theorem 3 is useful). (a) T: R3

Question:

Verify that each of the following is an isomorphism (Theorem 3 is useful).
(a) T: R3 → R3; T(x, y, z) = (x, x + y, x + y + z)
(b) T: Mmn → Mmn; T(X) = UXV, U and V any vector space
(c) T: V → V; T(v) = kv, k ≠ 0 a fixed number, V any vector space
(d) T: Mmn → Mnm; T(A) =AT