Question

let * be a binary operation on R defined by a*b =a+b-2ab.then find the value of 4*3​

Answer 1

Given, * is a binary operation on R defined by a*b=a+b-ab

Let. Then

Thus,So, * is a binary operation on R.

Now,

Commutativity :we have,

So, * is commutative on R

Associativity :, we have,

So, * is associative on R

Identity Element : Let e be the identity element in R, then

So, 0 is the identity element in R.

Inverse of an Element : Let a be an arbitrary element of R and b be the inverse of a. Then,

This inverse exist only if So, every element of R is invertible except -1.

Answer 2

a*b =a+b-2ab

Therefore,

4*3= 4+3-2*4*3

=7-24

=-17