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Let h belong to H ≤ G; prove that hH=H=hH. and Let a, b ∈ G...

Let h belong to H ≤ G; prove that hH=H=hH.

and

Let a, b ∈ G = group and H ≤ G; prove that if aH = Hb, then aH = Ha and bH = Hb.

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