Problem 1.3. For invertible square matrices A,B,C of the same size, (a) prove that C-¹B-¹A-¹ is the inverse of ABC and (b) assuming AB: BA, prove that (A + B)³ = A³+3A²B+3AB²+ B³.
Problem 1.3. For invertible square matrices A,B,C of the same size, (a) prove that C-¹B-¹A-¹ is the inverse of ABC and (b) assuming AB: BA, prove that (A + B)³ = A³+3A²B+3AB²+ B³.
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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Transcribed Image Text:Problem 1.3. For invertible square matrices A,B,C of the same size,
(a) prove that C-¹B-¹A-¹ is the inverse of ABC and
BA, prove
prove that
(b) assuming AB =
(A + B)³ = A³ +3A²B+3AB² + B³.
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