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(1) If AB= 0, then A=0 or B=0. (2) If A² = I, then A = I or A = -1. (3) AB = BA

(1) If AB= 0, then A=0 or B=0. (2) If A² = I, then A = I or A = -1. (3) AB = BA

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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True false 1 to 5
(1) If AB O, then A= O or B=0. (2) If A² I, then A = I or A=-I. (3) AB=BA (4) If AB (5) A(BC) = (AB)C (6) (AB)' = B' A' AC, then B = C. (7) A+ A' is symmetric. (8) A-A' is skew-symmetric. (9) If A and B are symmetric, then so is AB. (10) If A = (a)nxn is skew-symmetric, then a=0 for all 1 ≤ i ≤n. (11) tr(A + B)= tr(A) + tr(B) (12) tr(aA) = a"tr(A), where a € R and A has size n x n. (13) tr(AB) = tr(A)tr(B) (14) tr(AB) = tr(BA) (15) tr(AA) = (tr(A))2 (16) There exist square matrices A and B such that AB-BA=I.
Transcribed Image Text:(1) If AB O, then A= O or B=0. (2) If A² I, then A = I or A=-I. (3) AB=BA (4) If AB (5) A(BC) = (AB)C (6) (AB)' = B' A' AC, then B = C. (7) A+ A' is symmetric. (8) A-A' is skew-symmetric. (9) If A and B are symmetric, then so is AB. (10) If A = (a)nxn is skew-symmetric, then a=0 for all 1 ≤ i ≤n. (11) tr(A + B)= tr(A) + tr(B) (12) tr(aA) = a"tr(A), where a € R and A has size n x n. (13) tr(AB) = tr(A)tr(B) (14) tr(AB) = tr(BA) (15) tr(AA) = (tr(A))2 (16) There exist square matrices A and B such that AB-BA=I.
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