Question

(i) A binary operation * defined Q – {1} is given by a * b = a + b – ab. Find the identity element.

Answer 1

Dear student
$$\begin{gathered} a*b=a+b-ab \\ Letebetheidentityelement. \\ So,a*e=e*a=a \\ \Rightarrow a+e-ae=e+a-ea=a \\ \Rightarrow a+e-ae=a \\ \Rightarrow e-ae=0 \\ \Rightarrow e\left(1-a\right)=0 \\ \Rightarrow e=0 \\ So,0istheidentityelement \end{gathered}$$
Regards