Because multiplication is the converse of division, just like addition is the converse of subtraction.
If a/b=c, then a=bc. If a divided by b is equal to c, then a equals b times c. These are the rules of arithmetic. If they weren't true the universe would fall apart! The rule can be used as a check that you have the right answer. However, the rule doesn't allow you to divide by zero. That's a no-no.