Let H be a subgroup of G and let a, b ? G. If aH = bH, then * Ha^-1 = Hb^-1 Ha^-1 = Hb^-1 Ha = Hb None of the choices a^-1H = b^-1H a^-1H = b^-1H
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Since aH = bH, for any h ∈ H, there exists an element h' ∈ H such that ah = bh'. Now, we want to find an element in Ha^{-1} and show that it is also in Hb^{-1}. Consider the element a^{-1}(ah) = a^{-1}(bh'). Since h and h' are in H and H is a subgroup, a^{-1}h ∈ Show more…
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