*28*

*Group theory*

**28.1***For each of the following sets, determine whether they form a group under the* *operation indicated (where it is relevant you may assume that matrix multiplication* *is associative):*

(a) *the integers (mod* 10*) under addition*;

(b) *the integers (mod* 10*) under multiplication*;

(c) *the integers* 1, 2, 3, 4, 5, 6 *under multiplication (mod* 7*)*;

(d) *the integers* 1, 2, 3, 4, 5 *under multiplication (mod* 6*)*;

(e) *all matrices of the form*

*where a and b are integers (mod* 5*) and a* ≠ 0 ≠ *b, under matrix multiplication*;

(f) *those elements of ...*

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