For each of the following cases determine whether (A, +, x) is

(a) a ring,

(b) a ring with unity,

(e) a commutative ring.

In (i), (ii) and (iii) + and x are ordinary matrix addition and multiplication.

(i) A = the set of all 3 x 3 matriees with entries in Z.

(ii) A = the set of all 2 x 2 matrices with entries in Z, of the form

(iv) A = the set of all finite subsets of N, + is EIJ, the symmetrie differenee or 'exclusive or' operator, and x is n.

Transcribed Image Text:

(iii) As for (ii), but of the form a [[] b I [8] 0