# Example of non-commutative ring without unit such that...

Give an example of a non-commutative ring without unity such that $(xy)^2=x^2y^2$, for all $x,y\in R$.

• Feb 22 '15 at 11:05

In the ring of $2\times2$ matrices with even entries, considered modulo $16$, we have $ABCD=0$ for all elements $A,B,C,D$. No unit element, not commutative.