Look at -a first.



Add a:  -a + a = 0   (by the definition of the additive inverse)





Look at -1(a) next.

Add a:  -1(a) + a

Factor:  = a(-1 + 1)

Simplify: = a(0) = 0



This has shown  -1(a) + a = -a + a,  thus  -1(a) = -a and the proof is

complete. 

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