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# Find which of the operations given below has identity: $(iii)\;\; a \ast b = a+ab$

This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com

Toolbox:
• An element $e \in N$ is an identify element for operation * if $a \ast e=e \ast a$ for all $a \in N$
Given $a * b =a+ab$
Let e be an identity element
We know that $a \ast e = a, a \neq 0$
Now from the given definition of operation * we have a*e =a + ae => a=a+ae
Also e*a = a => a=e+ae
Since $a \ast e$ is not equal to $e \ast a$ , the operation given by $a * b =a+ab$ has no identity.