Let A and B be two $3\times 3$ matrices such that AB = BA. Further, if $A\ne B^4$ and $A^2=B^8$ , then which of the following is/are correct?

 $(A-B^4)(A+B^4)=\mathrm{0...}\left(1\right)\because AB=BA$
 $\Rightarrow |A+B^4||A+B^4|=0$
Now if  $|A+B^4|\ne 0\Rightarrow A\_B^4=0\text{ by (1)}$
Which is not possible  $\therefore |A+B^4|=0$
Which is like matric C for which $(A+B^4)C=0$ so A, C, D are correct