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Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition by M. P. Hobson, K. F. Riley

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28

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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

image

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

(f)  those elements of ...

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