Hermitian Matrix?

Question

Consider the following 3*3 matrix

2 2+i 0
a 4 2i
b c 6

Find values of a,b and c if the matrix is:
(i) Hermitian
(ii) Skew Hermitian

Answer 1

Denoting the conjugate of a with a*, we have that if the matrix is hermitian, then a = (2+i)* = 2-i, b = 0* = 0, and c = (2i)* = -2i.

It is impossible for the given matrix to be skew-hermitian because the entries on the main diagonal are not pure imaginary.