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5. Let A, Be M¸. Show that I. If A is idempotent, then P'AP is idempotent for any invertible PeM,: (1+ A) is idempotent if and only if A is involution. II.

5. Let A, Be M¸. Show that I. If A is idempotent, then P'AP is idempotent for any invertible PeM,: (1+ A) is idempotent if and only if A is involution. II.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.2: Integral Domains And Fields
Problem 18E: [Type here] 18. Prove that only idempotent elements in an integral domain are and . [Type here]
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5. Let A, B e M,. Show that I. If A is idempotent, then P-'AP is idempotent for any invertible РеМ, (I+ A) is idempotent if and only if A is involution. II.
Transcribed Image Text:5. Let A, B e M,. Show that I. If A is idempotent, then P-'AP is idempotent for any invertible РеМ, (I+ A) is idempotent if and only if A is involution. II.
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