( -1 + 1 ) = 0, definition of additive inverse
( - 1 )( -1 + 1 ) = 0, multiplicative property of zero
( -1 )( -1 ) + ( -1 )( 1 ) = 0, Distributive property
( -1 )( -1 ) + ( -1 ) = 0, Multiplicative property of 1
Therefore ( -1 )( -1 ) = 1, (-1 ) has a unique additive inverse 1.