3. Show that if A and B are such that B = C-¹AC for some invertible matrix C, then det(A) = det (B) and that A and B have the same characteristic polynomial.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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3. Show that if A and B are such that B = C-¹AC for some invertible matrix C, then det(A) =
det (B) and that A and B have the same characteristic polynomial.
Transcribed Image Text:3. Show that if A and B are such that B = C-¹AC for some invertible matrix C, then det(A) = det (B) and that A and B have the same characteristic polynomial.
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