Unformatted text preview: Show that the usual formula yields the inverse of A .] c. Conclude that A ∈ M 2 ( R ) × if and only if det( A ) ∈ R × . Exercise 3. Given that Z × n = U ( n ) for n ≥ 2, prove that Z × n = Z n { } if and only if n is prime. This completes the proof that Z n is a ﬁeld if and only if n is prime. Exercise 4. Let A = ² 1 32 4 ³ . Determine if A is a unit in M 2 ( R ) for the following choices of R . a. R = Q b. R = Z c. R = Z n (your answer will depend on n )...
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 Spring '10
 RyanDaileda
 Algebra, Vector Space, c., Abelian group, Algebraic structure

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