Answer:

Hence, the composition table is as follows:

Answer:

Hence, the composition table is as follows:

Answer:

Hence, the composition table is as follows:

Answer:

Hence, the composition table is as follows:

Answer:

Hence, the composition table is as follows:

We observe that the elements of the first row are the same as the top most row. So, is the identity element with respect to

Finding inverse of

From the above table we observe,

Hence the inverse of is

Answer:

Hence, the composition table is as follows:

We observe that the elements of the first row are the same as the top most row. So, the identity element is 1.

Question 7: Find the inverse of 5 under multiplication modulo 11 on

Answer:

Hence, the composition table is as follows:

We observe that the elements of the first row are the same as the top most row. So, the identity element is 1.

Question 8: Write the multiplication table for the set of integers modulo 5.

Answer:

Hence, the composition table is as follows:

Show that both the binary operations are commutative and associative. Write down the identities and list the inverse of elements.

Answer:

(i) We observe the following:

There is commutative.

Hence, is associative too.

Therefore, to find the identity element, we need:

(ii) We observe the following:

There is commutative.

Hence, is associative too.

Therefore, to find the identity element, we need:

We find that there is no unique element which satisfies the condition.

Since the identity is not unique, the inverse will also be not unique.

Show that is the identity for this operation and each element of the set is invertible with being the inverse of **[CBSE 2011]**

Answer:

The operation is defined as

Thus, is the identity element for the given operation