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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
cbse
class12
bookproblem
easy
ch1
sec4
p25
q10
q10-3
sec-a
math
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asked
Mar 19, 2013
by
meena.p
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1 Answer
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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.
answered
Mar 20, 2013
by
thagee.vedartham
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