Each element of an integral domain has no more than 2 square roots. The difference of two squares identity is proved using the commutativity of multiplication. If and are square roots of the same element, then . Because there are no zero divisors this implies or , where the latter means that two roots are additive inverses of each other. In other words if an element a square root of an element exists, then the only square roots of are and . The only square root of 0 in an integral domain is 0 itself.