Originally Posted by

**flabbergastedman** We are given R/I, where

R:= {$\displaystyle \left(\begin{array}{cc}q&r\\0&s\end{array}\right) $: q,r,s are in the rational numbers} and I:={$\displaystyle \left(\begin{array}{cc}0&r\\0&s\end{array}\right)$: r,s also in the rational numbers}

and the defined set of I forms an ideal of R

I'm not sure where to even start. I know for other quotient rings, it was a question of finding factors of the "denominator" - if any existed, then it could not be a field since it would not be irreducible. But since we're dealing with an ideal, I'm not so sure. I've tried finding zero-divisors, but at this point it seems a fruitless exercise, so I turn to your collective expertise.