Q1) Are these rings,

a) 3Z X Z (direct product) and

b) {ab(sqrt3)|a,bEQ}

I think a) is a ring because 3Z and Z are rings and b) is not a ring as it is not a group because sqrt3 is irrational.

Q2) Consider the matrix ring M2(Z2)

a) Find the order of the ring

b) List all the units of the ring

Please show me what the matrix looks like as well because i think thats whats causing the problem.

Thanks