K KLHON Apr 2018 10 0 Hong Kong Dec 12, 2019 #1 Let A, B be two different nxn square matrices and that their inverses do not exist. Under what conditions do rank(AB) = rank(BA) Thanks for your help Sincerely yours Edmond

Let A, B be two different nxn square matrices and that their inverses do not exist. Under what conditions do rank(AB) = rank(BA) Thanks for your help Sincerely yours Edmond

I Idea Jun 2013 1,127 601 Lebanon Dec 12, 2019 #2 This might help (if it is a correct formula) \(\displaystyle \text{rank}(B A)=\text{rank}(A)-\dim (\ker B\cap \text{range} A)\)

This might help (if it is a correct formula) \(\displaystyle \text{rank}(B A)=\text{rank}(A)-\dim (\ker B\cap \text{range} A)\)