We need to verify if this is a subring with or without identity of M(R). The book says it is without identity, but I am confused.
It is:
all 2x2 matrices of the form (0 r; 0 0) for r rational.
I don't see how this doesn't have identity since (0 r; 0 0)* (1 0; 0 1)=(0 r; 0 0)
Thanks.