Compute the product in the given ring:

(12)(16) in $$\mathbb{Z}_{24}$$

I know the answer is 0 because it's in the book, but what exactly am I being asked here? I tried it as a product of transpositions and didn't find that helpful, then tried just multiplying them as mod 24 but assuming that I'm doing that right, I get 8. So I'm not sure what the problem is actually asking me.

Question

Compute the product in the given ring:

(12)(16) in $$\mathbb{Z}_{24}$$

I know the answer is 0 because it's in the book, but what exactly am I being asked here?  I tried it as a product of transpositions and didn't find that helpful, then tried just multiplying them as mod 24 but assuming that I'm doing that right, I get 8.  So I'm not sure what the problem is actually asking me.

anonymous · Answer

i dont really know what its asking, 
but multiplying them mod 24 would give 0 wouldn't it?

12*16 = 12*2*8 = 24*8

chriss · Answer

yeah ok.  I was doing my mod arithmetic incorrectly.  

Thanks!

anonymous · Answer

no problem :)