Show that each matrix type is normal.
Now use the definitions for the six cases stated and plug them into the above definition to show they are normal:
1. Hermitian, A^t = A , so
[A , A^t] = A A^t - A^t A = A A - A A = 0
2. skew-Hermitian, A^t = -A , so
[A , A^t] = A A^t - A^t A = - A A + A A = 0
3. unitary, A^t = A^i
[A , A^t] = A A^t - A^t A = A ...