Thread: integral domain problem...

Q: let R be a ring of 2 by 2 matrices with integer entries.which of the following subset of R is integral domain?
a) M(0,x,y,0)
b)M(x,0,0,y)
c)M(x,0,0,x)
d)M(x,y,y,z)
where M stands matrix of elements taken row by row.

Originally Posted by Mathventure

Q: let R be a ring of 2 by 2 matrices with integer entries.which of the following subset of R is integral domain?
a) M(0,x,y,0)
b)M(x,0,0,y)
c)M(x,0,0,x)
d)M(x,y,y,z)
where M stands matrix of elements taken row by row.

Here you just need to apply the definitions of an integral domain.

Say that (in first case) so which means and so . So the only way to get the zero matrix is to have zero matrices in the very beginning. Try the same approach for the other three.