# Math Help - Ideals of ring of square matrices having rational entries...

1. ## Ideals of ring of square matrices having rational entries...

set of all $2*2$ matrices forms a ring

I want to prove that its only Ideals are Zero matrix and ring itself.

How to prove it??

set of all $2*2$ matrices forms a ring
More generally, every two sided ideal of matrix ring $M_n(R)$ is equal to $M_n(I)$ for some two-sided ideal I of R. Since Q is a field, its ideals are (0) and Q itself. Now the conclusion follows.