"-a=(-1)·a for all a [in] R. For ..." (see ita-2-1-18-pg19)
"... so that (-1)·a and -a are both solutions of the equation x+a=0, hence are equal." (see ita-2-1-18-pg19)
Note that, in Mathematica, multiplication has a higher 'precedence' than addition so that in the first example below the multiplication is done first and then the addition occurs. In the second example the a's are added first because they are within parentheses.