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).

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.5: Determinants
Problem 82E: Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.
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Solve only b) please thank you

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).
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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