Q. 10 Find which of the operations given above has identity.

Answers (1)

An element  p \in Q will be identity element for operation *

if a*p = a = p*a   for all a \in Q

(v) a * b = \frac{ab}{4}

  a * p = \frac{ap}{4}

  p * a = \frac{pa}{4}

a*p = a = p*a    when  p=4  .

Hence, (v) a * b = \frac{ab}{4}  has identity as 4.

However, there is no such element  p \in Q  which satisfies above condition for all rest five operations.

Hence, only (v) operations have identity.

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