Let * be any binary operation on a set A. An element a' ϵ A is called an inverse of a ϵ A for the binary operation *, if
a * a' = a = a' * a
a * e = a' = e * a
e * a' = a = a' * e
a * a' = e = a'* a
Let * be any binary operation on the set R defined by a * b = a + b – ab, then the binary operation * is