4. If A and B are n x n invertible matrices and c ER, prove or disprove the following statements. (a) det (In) = 1 (d) det (A) = det (AT) (b) det (A-¹) = det(A)-¹ (e) det (A + B) = det (A) + det (B) (c) det (A-¹BA) = det (B) (f) det (CA) = [c]" det(A)
4. If A and B are n x n invertible matrices and c ER, prove or disprove the following statements. (a) det (In) = 1 (d) det (A) = det (AT) (b) det (A-¹) = det(A)-¹ (e) det (A + B) = det (A) + det (B) (c) det (A-¹BA) = det (B) (f) det (CA) = [c]" det(A)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...
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