Question #141537
|a|=(2*n+1);
aba^(-1)=b^(-1);
b^2=?
1
Expert's answer
2020-11-02T19:07:15-0500

Given that,

a=2n+1 and aba1=b1|a|=2^{n+1} \ and \ aba^{-1}=b^{-1}

we have to find b2=?b^2=?

since aba1=b1    (aba1)1=(b1)1aba^{-1}=b^{-1} \implies (aba^{-1})^{-1}=(b^{-1})^{-1}

    ab1a1=b\implies ab^{-1}a^{-1}=b

    (ab1a1)2=b2\implies (ab^{-1}a^{-1})^2=b^2

    b2=ab1a1ab1a1\implies b^2=ab^{-1}a^{-1}ab^{-1}a^{-1} =ab2a1=ab^{-2}a^{-1}


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