I was doing linear algebra problems and got stuck in the following question:
Let $A$ and $B$ be $n\times n$ matrices such that $A^2 B^2=0$. Then which of the following option is correct? (and why?)
(a) $B^2 A^2=0$
(c) Either $A^2=0$ or $B^2=0$
(d) Either $A$ or $B$ has $0$ determinant
It would be helpful if any of you could provide a counterexample for the incorrect options. Thanks...