If defined, they are inverse operations. However, multiplication and division is a somewhat flawed example because division by 0 is not defined.
So, if you have a number x, then x*0 = 0 but 0/0 is not x: it is not defined.
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I would just call them "multiplication" and "division". Both are examples of arithmetic operations.
It is the order of arithmetical operations and is known as BODMAS or BIDMAS meaning brackets, indices, division, multiplication, addition and subtraction
Informally, many people would call the opposites. But the correct math term is inverse operations. Addition is the inverse operation of subtraction and multiplication if the inverse operation of division.
It is known as BIDMAS (UK) or PEMDAS (US) BIDMAS = Brackets, Index, Division, Multiplication, Addition, Subtraction. or PEMDAS = Parentheses, Exponent, Multiplication, Division, Addition, Subtraction. There is no porder between DM/MD and between AS: Division and multiplication are to be carried out left to right. Addition and subtraction are to be carried out left to right.
A product is an answer to a multiplication problem.