A variant of a problem from Halmos :
If AB=C and BA=D then explain why (C-D)^2 is commutative with all 2x2 matrices if A and B are 2x2 matrices.
This result does not hold for any other nxn matrices where n > 2. Explain why.
Edit: I tried to show that ((C-D)^2) E - E((C-D)^2) is identically...