es m- Exercise 2.3.34 If A and B are n x n matrices, show that: a. AB = BA if and only if (A+B)² = A²+2AB+B². b. AB = BA if and only if (A+B) (A-B) = (A - B) (A + B).
es m- Exercise 2.3.34 If A and B are n x n matrices, show that: a. AB = BA if and only if (A+B)² = A²+2AB+B². b. AB = BA if and only if (A+B) (A-B) = (A - B) (A + B).
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:es
m-
Exercise 2.3.34 If A and B are n x n matrices,
show that:
a. AB = BA if and only if
(A+B)² = A²+2AB+B².
b. AB = BA if and only if
(A+B) (A-B) = (A - B) (A + B).
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