Let $M$ and $N$ be two $3 \times 3$ matrices such that $MN = NM$. Further, if $M \neq N^2$ and $M^2 = N^4$, then\\
(A) determinant of $\left(M^2 + MN^2\right)$ is 0\\
(B) there is a $3 \times 3$ non-zero matrix $U$ such that $\left(M^2 + MN^2\right)U$ is the zero matrix\\
(C) determinant of $\left(M^2 + MN^2\right) \geq 1$\\
(D) for a $3 \times 3$ matrix $U$, if $\left(M^2 + MN^2\right)U$ equals the zero matrix then $U$ is the zero matrix