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Could any one tell me how to show that only ideals of above ring are $(0)$ and the whole ring?

My thought was to show that by taking any proper ideal if we can prove identity element belongs to it then we can generate the whole ring? Thanks for helping

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In general, the two-sided ideals of $M_n(R)$ are given by $M_n(I)$ where $I$ is an ideal of $R$.

I assume that $Q$ is $\mathbb Q$, which is a field. In this case, you know all its ideals.

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