set of all $\displaystyle 2*2$ matrices forms a ring
I want to prove that its only Ideals are Zero matrix and ring itself.
How to prove it??
Thank you in advance
More generally, every two sided ideal of matrix ring $\displaystyle M_n(R)$ is equal to $\displaystyle M_n(I)$ for some two-sided ideal I of R. Since Q is a field, its ideals are (0) and Q itself. Now the conclusion follows.