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Unformatted text preview: of Z 5 . 2. (a) Give the addition and multiplication tables for Z 9 with the usual addition and multiplication as deﬁned in class. i). Is Z 9 with the usual addition and multiplication a ﬁeld? If your answer is yes, then: ii). Find the additive inverses of each element of Z 9 . iii). Find the multiplicative inverses of each nonnegative element of Z 9 . 3. Is the set M 2x2 of all 2 x 2 invertible matrices, with the usual matrix addition and multiplication a ﬁeld? Justify your answer. 4. Is the set Q [ √ 7] = { a + b √ 7  a, b ∈ Q } with addition and multiplication deﬁned by: ( a + b √ 7) ⊕ ( c + d √ 7) = ( a + c ) + ( b + d ) √ 7 for all a, b, c, d ∈ Q ( a + b √ 7) ⊗ ( c + d √ 7) = ( ac + 7 bd ) + ( ad + bc ) √ 7 for all a, b, c, d ∈ Q a ﬁeld? 5. Section 3 . 1 : #2 , 6 , 14 , 18...
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This note was uploaded on 12/20/2010 for the course MAT MATB24 taught by Professor X.jiang during the Spring '10 term at University of Toronto.
 Spring '10
 X.Jiang
 Math, Linear Algebra, Algebra

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