Please, show me all the steps and explanations for each of the questions below (please answer all parts a thru g), thank you very much!

Let the two by two matrix A = 2 1 i

1 + i 1

(a) Find the eigenvalues of A

(b) Find the eigenvectors of A: u1 and u2

(c) Normalize u1 and u2

(d) Form a matrix U = [u1, u2] based on your results from (c)

(e) Find U^H U (Note in U^H H stands for Hermitian matrix.)

(f) Find U^H AU

(g) What can you say about the matrix U and relation to the matrix A