Prove that: If A or B is nonsingular, then AB is similar to BA

banganX

banganX

Answered question

2020-11-08

Prove that: If A or B is nonsingular, then AB is similar to BA

Answer & Explanation

diskusje5

diskusje5

Skilled2020-11-09Added 82 answers

If there is an invertible matrix P that can be used to compare two matrices M and N, we can say that they are similar. P1MP=N
Assume A is not single. So, A1 exist. Now AB=AB(AA1)=A(BA)A1
This demonstrates how AB and BA are comparable.

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