As we know, multiplication of integers may be defined in terms of addition . This is why Euclid did not mention multiplication among his Common Notions . Properties of multiplication are derivable from those of addition and, therefore, if we can add equations, we may multiply them as well. It's interesting that Euclid stipulates among Common Notions not only validity of addition but also that it's permissible to subtract equal quantities from equal quantities without disturbing their equality. A legitimate question is whether the same is true of multiplication and the operations inverse to multiplication.
Division is one operation that reverses the result of multiplication.
However, concealed division by 0 results in errors and what's commonly known as arithmetic paradoxes . Another case of reversing the result of multiplication is squaring. As in the case of division, squaring should be used cautiously. If two numbers are equal, their squares are also equal. Assume the answer is unqualified yes and let's see where this will lead us.