There is no "operation of integers".
There are some operations that can be defined for single integers such as: additive inverse (= negative), multiplicative inverse (= reciprocal, not defined for 0), absolute value, square, cube, nth power, square root (if non-negative), cube root and so on.
Then there are operations that can be defined for two integers, such as sum, difference, absolute difference, product, quotient (if the second integer is not 0), exponent, logarithm of one to the other as base (if they are both positive), and so on.
Addition and multiplication are operations on integers that are commutative.
Part 2
I am not sure there are any fundamental operations of integers. The fundamental operations of arithmetic are addition, subtraction, multiplication and division. However, the set of integers is not closed with respect to division: that is, the division of one integer by another does not necessarily result in an integer.
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Addition, subtraction and multiplication.
add, subtract, multiply, divide
basic opration of inntegers
Because different operations with different integers give different answers.
The Diagram of Integers typically refers to a visual representation of integers on a number line. In this diagram, integers are arranged in a straight line, with positive integers extending to the right of zero and negative integers extending to the left. This helps illustrate the relationships between different integers, such as their order and magnitude. It is a useful tool for understanding basic arithmetic operations and concepts involving integers.
There are an infinite number of operations for integer and different rules will apply for different operations. The question needs to be more specific.
All numbers - integers as well as non-integers - are combined using different mathematical operations. Some operators are binary: that is, they combine two numbers to produce a third; some are ternary (combine 3 to produce a fourth) and so on.The set of integers is closed under some operations: common examples are addition, subtraction, multiplication, exponentiation. But not all operators are: division, for example.
I am not at all sure that there are any rules that apply to integers in isolation. Any rules that exist are in the context of binary operations like addition or multiplication of integers.