Answer :

e is the identity of * if e*a = a



From the above Venn diagram,


A*X = AX = A


X*A = XA = A


X is the identity element for binary operation *


Let B be the invertible element


A*B = X


AB = X


This is only possible if A = B = X


Thus X is the only invertible element in P(X)


Hence proved.


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