Q15 of 123 Page 3

A binary operation * is defined on the set R of all real numbers by the rule for all a, b ∈ R. Write the identity element for * on R.

The given binary operation is a*b =

We have to find the identity element for the above relation.


Let that element be e.


∴ From the definition of identity element ,


a*e = a


∴ = a


Squaring both sides, we get,


=


∴ e = 0


Thus, the identity element for this operation is 0.


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