Maximal abelian subalgebras of $B(\mathcal{X})$

Let $\mathcal{X}$ be an infinite dimensional complex Banach space and $B(\mathcal{X})$ be the Banach algebra of all bounded linear operators on $\mathcal{X}$. Żelazko [1] posed the following question: Is it possible that some maximal abelian subalgebra of $B(\mathcal{X})$ is finite dimensional? Interestingly, he was able to show that there does exist an infinite dimensional closed subalgebra of $B(\mathcal{X})$ with all but one maximal abelian subalgebras of dimension two. The aim of this note is to give a negative answer to the original question and prove that there does not exist a finite dimensional maximal commutative subalgebra of $B(\mathcal{X})$ if $\text{dim}X=\mathrm{\infty }$.