What characterizes an identity element in arithmetic?

An identity element in arithmetic is defined as a value that, when used in an operation with any number, leaves the original number unchanged. For example, in addition, the identity element is zero, because adding zero to any number does not alter its value. Similarly, in multiplication, the identity element is one; multiplying any number by one results in the original number being unchanged. This property is fundamental in various branches of mathematics and is crucial for understanding operations and functions.

The other characteristics do not align with the definition of an identity element. For instance, an element that changes the value or produces a different result is not an identity at all, as it does not fulfill the identity's basic requirement. The notion that it always results in zero applies specifically to the addition identity but does not encompass the broader definition applicable to multiplication or other operations.