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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