Q. 75.0( 1 Vote )

# Prove that the operation * on the set

defined by A*B=AB is a binary operation.

Answer :

Given that * is an operation that is valid on the set and it is defined as given:A*B = A B.

According to the problem it is given that on applying the operation * for two given numbers in the set ‘M’ it gives a number in the set ‘M’ as a result of the operation.

⇒ A*B∈M ...... (1)

Let us take here a∈R, b∈R, c∈R and d∈R then,

⇒

⇒

⇒

⇒

Since a∈R and c∈R then ac∈R

And also b∈R and d∈R then bd∈R.

⇒ AB∈R

∴ The operation ‘*’ defines a binary operation on ‘M’.

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