The units of a cartesian product?

[chuy52506]

Find all units in $$Z$$₁₂ X $$Z$$₆ and their inverses.

What i did was find the units of Z₁₂ which are 1,11,5,7 then the ones of Z₆ which are 1,5 and take the cartesian product of those two sets?

 

[micromass]

Yes, that would be correct!

 

[chuy52506]

So there would be eight?
1,1 1,5 11,1 11,5 5,1 5,5 7,1 and 7,5?

 

[Landau]

Instead of asking this, why don't you try to prove that the units of the product are precisely the pairs of units?

 

[chuy52506]

Because it helps to do an example before. So is this correct?

 

[Landau]

micromass already answered that question. If you're still not entirely sure, my advice stands: prove it! (it's quite easy; it's a matter of writing out the definitions)