They are not the same!
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Those are the rules of multiplication (and division).
The rules are not the same.Multiplication is commutative whereas division is not.Multiplication is associative whereas division is not.
It is true, and it follows from the definition of multiplication and division.
When multiplying integers, multiplying by the same sign will always produce a positive integer. Such as a negative times a negative equals a positive. If the signs are different then the product will be a negative.
They are all numbers and obey the same rules for addition, subtraction, multiplication, division, exponentiation etc.