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Question 3. Let A and B be nxn matrices. Show that (a) (A - A¹)³ is skew-symmetric. (b) (AB+B¹A¹)4 is symmetric. (c) AB = BA if and only if A¹B = B¹A¹.

Question 3. Let A and B be nxn matrices. Show that (a) (A - A¹)³ is skew-symmetric. (b) (AB+B¹A¹)4 is symmetric. (c) AB = BA if and only if A¹B = B¹A¹.

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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please  may you answer question 3

Question 1. Let A = 3-2 2 -1 0 00 Question 2. Let k = 2, A = and B= 3 0 2 4 Find A³. [ ]. 1 0 1 -1 10 Question 3. Let A and B be nx n matrices. Show that Show that A(kB) = (kA)B= k(AB). (a) (A- A+)³ is skew-symmetric. (b) (AB + B¹ At) is symmetric. (c) AB = BA if and only if A¹Bt = Bt At.
Transcribed Image Text:Question 1. Let A = 3-2 2 -1 0 00 Question 2. Let k = 2, A = and B= 3 0 2 4 Find A³. [ ]. 1 0 1 -1 10 Question 3. Let A and B be nx n matrices. Show that Show that A(kB) = (kA)B= k(AB). (a) (A- A+)³ is skew-symmetric. (b) (AB + B¹ At) is symmetric. (c) AB = BA if and only if A¹Bt = Bt At.
Expert Solution
Step 1: Finding the skew symmetric matrices

Given that A and B be n*n matrices.

Advanced Math homework question answer, step 1, image 1

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