Jambmaths question:
An operation *is defined on the set of real numbers by a * b = a + b + 1. If the identity element is –1 . Find the inverse of the element 2 under the operation
Option A:
4
Option B:
0
Option C:
–2
Option D:
–4
Jamb Maths Solution:
$\begin{align} & a*b=a+b+1 \\ & a*{{a}^{-1}}=e\text{ }\!\!\{\!\!\text{ }where {{a}^{-1}} is the inverse of a, e=identity element\} \\ & 2*{{2}^{-1}}=-1 \\ & 2*{{2}^{-1}}=2+{{2}^{-1}}+1=-1 \\ & 2+{{2}^{-1}}+1=-1 \\ & {{2}^{-1}}=-1-3 \\ & {{2}^{-1}}=-4 \\\end{align}$The inverse of 2 is –4
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