In School, students were taught that "if $m$ and $n$ are two non-negative integer, then their product $m \times n$ is equal to the sum of $n$, $m$-times or sum of $m$, $n$-times". If one of them is negative, then the principle still work. After this they were taught that "$ - \times - = +$", so the product of two negative integers is well defined. Does this follow from the above principle? Some people told me that it follows from the above principle, but i don't know how it follow. If someone ask you that how "$ - \times - = +$", what will be your answer?
Thanks in advance