I can not understand that how it is proved, so please somebody help me. I unable to prove but I think you will able to prove it.
Show that if two right cosets $Ha$ and $Hb$ are distinct then two left cosets $a^{-1}H$ and $b^{-1}H$ are distinct
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abstract-algebra
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2One way is to show that $Ha\to a^{-1}H$ is a bijection (or for this just injection is enough) between left and right cosets – 2017-02-14
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1Please prove in details. – 2017-02-14
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0is this about groups? – 2017-02-14
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1Yes this is about group – 2017-02-14
1 Answers
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As $Ha,Hb$ are equivalence classes, $Ha\neq Hb \iff a\notin Hb\iff ab^{-1}\notin H\iff (ab^{-1})^{-1}=ba^{-1}\notin H\iff a^{-1}\notin b^{-1}H\iff a^{-1}H\neq b^{-1}H$