This can be proved using the distributive law and the axiom that 1 is the multiplicative identity : for x real , we have where we used the fact that any real x times 0 equals 0 , implied by cancellation from the equation In other words , so ( − 1 ) · x is the arithmetic inverse of x , or − x . The square of − 1 , i.e. − 1 multiplied by − 1 , equals 1 .
So , for x real , we have where we used the fact that 0 multiplied by any real number x equals 0 , shown by cancellation from the equation In other words , so ( − 1 ) · x or − x is the arithmetic inverse of x . The square of − 1 , i.e. − 1 multiplied by − 1 , equals 1 .