Is the arithmetic mean relation of two sets of numbers hold for geometric and harmonic means?

Question

Let Aset= {a1,..an} and Bset={b1,..bn} be two sets of positive numbers.

AM - arithemtic mean, HM - harmonic mean, GM - geometric meam

If AM(Aset) >= AM(Bset) then GM(Aset) >= GM(Bset) ?

If HM(Aset) >= HM(Bset) then GM(Aset) >= GM(Bset) ?

If the answers are YES, please show me proofs.

Thanks in advance.