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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)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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)
Transcribed Image Text: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)
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