If A and B are any two matrices such that (A-B)^2=A^2-2 A B+B^2 then

$(A-B)^2=A^2-A B-BA+B^2 = A^2 - 2AB + B^2$

⇒   AB = BA       .....(1)

So   $A^2B = ABA$

$A^2 B^2=B A A B$

$A^2 B^2=B A B A$

$A^2 B^2=B^2 A^2$

Similarly 

$A^3 B^2=B^2 A^3$

$A^3 B^3=B^3 A^3$

$A^4 B^3=B^3 A^4$

⇒   $B^3 A^4-A^4 B^3=0$

Option C