# If a ring has zero divisors, is it necessarily commutative or non-commutative?

##### 1 Answer

Aug 27, 2016

A ring can have zero divisors whether or not it is commutative.

#### Explanation:

Consider arithmetic modulo

This is a commutative ring with

The ring of

For example:

#((1,0),(0,0))((0,0),(0,1)) = ((0,0),(0,0))#

#((1,1),(0,0))((1,0),(0,0)) = ((1,0),(0,0)) != ((1,1),(0,0)) = ((1,0),(0,0))((1,1),(0,0))#