Proof :

ok we can proof it by many way :

1) We Want Negative * Negative = Positive   

1 + (-1) = 0   

1 = (-1) * (-1)         End Of Proof (1).

2) Assume That      (-1) * (-1) = (-1)    Then,

(-1) [ 1 + (-1) ]  =  (-1) [ 1 + (-1) ]

(-1) [ 0 ]             = (-1) * (+1) + (-1) * (-1)

0                         =   (-1)            + (-1)

                 0 = (-2 ) ,      _{Contradiction ...}

So, (-1) * (-1)  Must Be Equal To   ( + 1)

End Of  Proof (2).

3) Let  x = ab + a(-b) + (-a) (-b)           Then ,

           x = ab +  ( -b)[ a + (-a) ]         , By Common Factor   ( بأخذ العامل المشترك)

           x = ab + 0    

           , x = a * b   >>>>>>>>>>>>  ( @ ).

   Now    x = ab + a(-b) + (-a) (-b)         For The Same X

               x = a [b + (-b) ] + (-a) (-b)

               x = 0 + (-a) (-b)

              , x = (-a) * (-b)  >>>>>>>>>>>> (@@).

From @ ,and @@   We Get That     x = a * b = (-a) * (-b)

                          That Means   a * b = (-a) *(-b)

                              Or           3 * 3 = (-3) * (-3)  =9 ....   End Of Proof (3).

END OF PROOF.