[Algebra] How to do arithmetic in the field Z_4?

Question

I have a trouble dealing subtraction in this. Suppose if we multiple 3 * 3 we get 9 and 9-4 = 5. Which is not in the field. How to solve this?

And if we have a negative number in as a result of a subtraction, for example -2 or -5. How we can tackle this?  I have encountered this situation while doing subtraction with the matrices in Z_4.

Answer 1

5 is also 1 in Z\_4

\-2 is 2 in Z\_4

\-5 is 3 in Z\_4

In modulo 4, you can add 4 and subtract 4 as many times as you want, and at some point, you should get a number in Z\_4. Of course, this applies for any field Z\_n, not only Z\_4