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If * is a binary operation defined in $Q^+$ as $a*b=\large\frac{ab}{3}$, then the inverse element of 4*6 is ?

$\begin{array}{1 1}\large\frac{9}{8} \\\large\frac{8}{9} \\ \large\frac{2}{3} \\ \large\frac{3}{2}\end{array}$

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Toolbox:
  • If $e\in Q^+$ is the identity element , then $a*e=a \:\:\forall\:a\in\: Q^+$
  • If $a*b=b*a=e$, where e is the identity element of * then b is inverse of a and viceversa.
Let e be the identity element then
$a*e=a\:\Rightarrow \large\frac{ae}{3}=a$
$\Rightarrow e=3$
$4*6=\large\frac{24}{3}=8$
Let $x$ be the inverse element of 8
Then $ 8*x=3$ $\Rightarrow\:\large\frac{8x}{3}=$$3$
$\Rightarrow\:x=\large\frac{9}{8}$

 

answered May 12, 2013 by rvidyagovindarajan_1
 

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