Lets assume (a.b)-1 = b-1.a-1
Then b-1.a-1 should be the inverse of a.b and there product should give the identity element e...
Now multiplying a.b and b-1.a-1 :
(a.b).(b-1.a-1) = e
a.(b.b-1).a-1 = e ............(As the group follows the Associative Property)
a.(e).a-1 = e
a.(e.a-1) = e
a.a-1 = e ......................(e.a-1 = a-1 as e is the identity element)
e = e
Hence L.H.S = R.H.S
And this Property Holds for the Groups....