Subring Test

[runescape09]

Let R = { martrix [a a (in the first row) b b (in the second row) | a,b∈Z }. Prove or disprove that R is a subring of M2(Z).

I've already know how to prove that R is the subring. But how do i show that their is an identity?

[Deveno]

if there IS an identity, wouldn't it have to be the same identity as M2(Z) has?

(note: some people require a ring to have identity, some people don't. by "identity" i mean multiplicative identity, as every ring MUST have a 0).

[runescape09]

if there IS an identity, wouldn't it have to be the same identity as M2(Z) has?

(note: some people require a ring to have identity, some people don't. by "identity" i mean multiplicative identity, as every ring MUST have a 0).

Okay, how do i know that the r is a ring?

[Deveno]

is (R,+) closed under matrix addition? if A is in R, is -A in R? is R closed under matrix multiplication? these are the crucial questions.

[runescape09]

is (R,+) closed under matrix addition? if A is in R, is -A in R? is R closed under matrix multiplication? these are the crucial questions.

isn't that proven by the subring test though?