A binary operation on the set is defined as

Show that 0 is the identity for this operation and each element a has an inverse

To find: identity and inverse element

contexto.140

3 years ago

For a binary operation if a*e = a, then e s called the right identity

If then is called the left identity

For the given binary operation,

which is less than 6

which is less than 6

For the condition,

But does not belong to the given set

So the identity element is 0

An element is said to be the inverse of a, if e where e is the identity element

a belongs to ,

– a belongs to

So c belongs to ,

So is not the inverse for all elements

Putting in the condition

=> belongs to the given set

Hence the inverse of the element a is (6-a)