50 points. can anyone give an example of a noncommutative ring that doesn't involve matrices?

Hamilton's quaternions are an example of non-commutative ring. If you are not familiar with them, they are similar to complex numbers, except for the fact that there are three roots of -1: the ring is generated by

Which means that a generic element is appears as follows:

The rules for additions are the usual: you sum like terms. As for the mutliplicaitons, you work like this:

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: