Why can you use addition to check a subtraction

So let's say the problem is 5 - 3, to keep it simple. The answer is 2. To use addition to check you would add 2 + 3 = 5. You can add the smaller numbers to get the one larger number. You can also do it with multiplication and division. For example, 5 * 3 = 15. You can divide 3 by 15 and get 5 or do 5 by15 and get 3.

Subtraction is the inverse (opposite) of addition. If the sum of the addition problem equals the number you subtracted from, the answer is correct and vice versa. The same goes for multiplication and division. 

Ex:
3 + 5 = 8
8 - 5 = 3 and 8 - 3 = 5

I hope this helps!