Question 201696
Let the product of any two negatives be given as {{{(-a)*(-b)}}}
{{{(-1)*a * (-1) *b}}}
{{{(-1)*(-1)*ab}}}
You 'know' the answer is {{{ab}}}
So what you really are asking is "Why is (-1) * (-1) = 1??? 

Let's 'prove it'
{{{0 = 0}}}
{{{(-1)*0 = 0}}}
{{{(-1)*(1+(-1))=0}}}
{{{(-1)*1 + (-1)*(-1) = 0}}} 
{{{-1 + (-1)*(-1) = 0}}}
{{{(-1)*(-1) = 1}}}

So there you have it.
Make sense?