The identity element of a group is an element that, when combined with any other element in the group, results in the same element. In other words, it leaves other elements unchanged when used in a group operation. It is typically denoted as "e" or "1".
The identity element is determined by the group's operation and its elements. It must satisfy the property that when combined with any element in the group, it results in the same element. This can be found by trial and error or through mathematical calculations.
Yes, the identity element is unique in a group. This means that there can only be one identity element in a group, and it is the same for all elements in the group.
The identity element is important in a group because it serves as the starting point for all group operations. It also helps in determining the inverse of an element and proving other properties of a group.
No, a group cannot have more than one identity element. If a group has two distinct identity elements, then they must be equal, as the identity element is unique in a group.