Suppose that T is n n and c, d are scalars. (a) Prove that if T

Question:

Suppose that T is n × n and c, d are scalars.
(a) Prove that if T has the eigenvalue λ with an associated eigenvector →v then →v is an eigenvector of cT + dI associated with eigenvalue cλ + d.
(b) Prove that if T is diagonalizable then so is cT + dI.