Use the properties det(AB) = det(A) det(B) and det(I n ) = 1 for n x

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Use the properties det(AB) = det(A) • det(B) and det(I_n) = 1 for n x n matrices to show the following:

a. Then x n matrices with determinant 1 form a normal subgroup of GL(n, R).

b. Then x n matrices with determinant ±1 form a normal subgroup of GL(n, R).

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Jan 02, 2023 04:46 AM

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Use the properties det(AB) = det(A) det(B) and det(I n ) = 1 for n x

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a Let H be the subset of GLn R consisting of the n n matrices with determinant 1 The property ...View the full answer

A First Course In Abstract Algebra

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