Jambmaths question:
An operation * is defined on the set of real numbers by $a*b=ab+2(a+b+1)$find the identity element
Option A:
-2
Option B:
-1
Option C:
2
Option D:
1
Jamb Maths Solution:
$\begin{align} & a*b=ab+2(a+b+1) \\ & a*e=ae+2(a+e+1)\text{ }\!\!\{\!\!\text{ }e\text{ is the identity element }\!\!\}\!\!\text{ } \\ & \therefore a*e=a \\ & ae+2(a+e+1)=a \\ & ae+2a+2e+2=a \\ & ae+2e=a-2a-2 \\ & e(a+2)=-a-2 \\ & e(a+2)=-(a+2) \\ & e=\frac{-(a+2)}{(a+2)}=-1 \\\end{align}$
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