let  A and  B be  square  matrices of order n  such that  Ax=Bx  and x belongs to Rn  then   find  rank  of A-B  and  show that  A and B  are identical

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...
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let  A and  B be  square  matrices of order n  such that  Ax=Bx  and x belongs to Rn  then  

find  rank  of A-B  and  show that  A and B  are identical

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