Thread: Ring with unity 1 that has subring with unity 1'

Hi, let me just say that I'm not in a class or anything, I'm just working through an old book and trying to understand.

Problem: Give an example of a ring with unity 1 that has a subring with unity .

So my ring must be not commutative or be such that not every nonzero element has a multiplicative inverse, since in a field "the unity element of a subfield must be the unity of the whole field." But I can't find an example. Thanks in advance!

let be the ring of all matrices with integer entries. Let then is a subring of and