A Banach algebra with trivial multiplication or the unitization of such an algebra is called by the author a trivial Banach algebra. He shows that the algebra \(B(X)\) of all continuous linear operators on the (real or complex) Banach space \(X\) always contains a maximal Abelian subalgebra that is trivial. In fact, he completely describes the class of trivial maximal Abelian subalgebras of \(B(X)\).