Let H be a subgroup of G, and let a belong to G. Then aH= H if and only if a belongs to H

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Group Theory | If a,bϵG and H any sub-group of G then Ha=Hb ⇔ ab^(-1) ϵH and aH=bH ⇔ b^(-1) aϵH | Group Theory | If a,bϵG and H any sub-group of G then Ha=Hb ⇔ ab^(-1) ϵH and aH=bH ⇔ b^(-1) aϵH |