Commutants of Endomorphism ring of simple AAA-modules [on hold]

Let AAA be a finite simple central kk algebra where kk is a field. Let MM be a simple AA module. Let f∈EndA(M)f \in End_A(M) commute with every element of EndA(M)End_A(M). How do I show f(x)f(x) is of the form axax for some fixed a∈Aa \in A?

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