I really got get around to doing tons of stuff this weekend…lots a work but I did prove this:

(-a)(-b)

=(-a + 0)(-b + 0)

=(-a + a – a)(-b + b – b)

=(-a)(-b) + (-a)(b) + (-a)(-b)

+(a)(-b) + (a)(b) + (a)(-b)

+(-a)(-b) + (-a)(b) + (-a)(-b)

=(-a)(-b+b-b+b) + (-b)(-a+a-a+a) +(a)(b)

=(-a)(0+0)+(-b)(0+0)+(a)(b)

=0+0+(a)(b)

=ab

so…(-a)(-b)=(ab) in any ring system…wheeeee…that’s the easiest damn question in the course 🙁