Given a finite field F, let M2(F) denote the set of all 2 Ã 2 matrices with
Question:
a) Determine the number of elements in M2(F) if F is
i) Z2 ii) Z3 iii) Zp, pa. prime
(b) As in Exercise 13 of Section 14.1, A =
M2(Zp) is a unit if and only if ad - be z. This occurs if the first row of A does not contain all zeros (that is, z's) and the second row is not a multiple (by an element of Zp) of the first. Use this observation to determine the number of units in
i) M2(Z2) ii) M2(Z3) iii) M2(ZP), p a prime
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Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
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