Question

findvthe identity element of the binary operations * defined on a*b = ab^2 ​

Answer 1

Explanation:

i) Let e be an identity element & a×e=e×a⟹a

2

+e

2

=e

2

+a

2

.

∴ There is no possible value of e where a

2

+e

2

=e

2

+a

2

.

ii) Let e be an identity element & a×e=e×a⟹(a−e)

2

=(e−a)

2

⟹a

2

+e

2

−2ae=e

2

+a

2

−2ae.

There is no possible value of e where a

2

+e

2

−2ae=e

2

+a

2

−2ae.

iii) Let e be an identity element & a×e=e×a=a⟹ae

2

=ea

2

=a⟹ae(e−a)=0

∴e=0 or e=a.