Is R Isomorphic to S? Finding an Explicit Isomorphism

[cagoodm]

Homework Statement

Determine whether R is isomorphic to S for each pair of rings given. If the two are isomorphic, find an explicit isomorphism (you do not need to show the formal proof). If not, explain why.

Homework Equations

R= 2x2 matrix, a 0, 0 b, for some integers a,b
S= Z x Z

The Attempt at a Solution

I know that they are both commutative under addition and multiplication, so I'm assuming they are isomorphic... but I have no idea how to find the explicit isomorphism.
Thank you

 

[micromass]

If I give you an element in ZxZ, say (a,b). Then you're given two integers a and b. How would you make a matrix in R with these two elements?