Question

Consider the binary operation * on Q definied by a*b=ab/6 find the identity of * on Q and inverse of the element 6 on Q

Answer 1

$Given \: a\ast b = \frac{ab}{6}$

$e \: is \: the \: identity \: of \: \ast if$

$\implies a \ast e = e\ast a = a$

$i.e., \frac{ae}{6} = \frac{ea}{6} = a$

$Which \: is \: possible \: if \: e = 6$

$\green { So, 6 \:is \:the \: identity \: element }$

$\green { of \: \ast}$

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