Browse Questions

# The identity element for the binary operation $\ast$ defined on $Q\sim \{0\}$ as $a\ast b=\large{\frac{ab}{2}} \normalsize \;a,b\in Q\sim\{0\}$ is

(A) 1 (B) 0 (C) 2 (D) none of these

Toolbox:
• 'e' is the identity element for binary operation * on Q-{0} if
• $a *e=e *a=a$
$a* b=\frac{ab}{2} \qquad a,b \in Q-\{0\}$

$a* b=a => \frac{ab}{2}=a$

$=> b=2$

$a*2=\frac{a.2}{2}=a$

$2*a=\frac{2.a}{2}=a$

e=2 is the identity element for * operation

'c' option is correct
edited Apr 1, 2016 by pady_1