Q. 75.0( 1 Vote )
Prove that the operation * on the set
defined by A*B=AB is a binary operation.
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.
∴ The operation ‘*’ defines a binary operation on ‘M’.
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