Moderate# Matrix Rings and Ideals

ABSALG-IEBDQN

Let $R$ be a ring. The *$n\times n$ matrix ring* over $R$, denoted by $M_n(R )$, consists of the set of all $n\times n$ matrices with entries from $R$, together with matrix addition and matrix multiplication.

Which of the following sets are either an ideal or a subring of $M_n(\mathbb{Q})$?