Let A = {1, 2, 3} and R = {(a,b): `a,b in A, a` divides b and b divides a}. Show that R is an identity relation on A.

Explanation

To show that the relation \( R \) is an identity relation on the set \( A = \{1, 2, 3\} \), we need to demonstrate that \( R \) consists only of the pairs where each element is related to itself. An identity relation on a set \( A \) is defined as \( R = \{(a, a) : a \in A\} \).

### Step-by-Step Solution:

1. **Define the Set and Relation**:
- Let \( A = \{1, 2, 3\} \).
- The relation \( R \) is defined as \( R = \{(a, b) : a, b \in A \text{ and } a \text{ divides } b \text{ and } b \text{ divides } a\} \).

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