If * is a binary operation defined as \(\rm a*b=\frac{ab}{2}\), then the identity element with respect to this binary operation is:

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AAI ATC Junior Executive 21 Feb 2023 Shift 1 Official Paper

Answer 1

Given:

\(\rm *\) is a binary operation defined as \(\rm a*b=\frac{ab}{2}\)

Concept:

Use property of identity

if e is the identity then

\(\rm e*a=a*e=a \)

Calculation:

Let \(\rm e\) is the identity then

\(\rm a*e=\frac{ae}{2} \)

\(\rm \implies a=\frac{ae}{2} \)

\(\rm \implies e=a\cdot\frac{2}{a} \)

\(\rm \implies e=2 \)

Hence the option (2) is correct.