Rank of product of two square matrices

Apr 2018
10
0
Hong Kong
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
 
Jun 2013
1,127
601
Lebanon
This might help (if it is a correct formula)

\(\displaystyle \text{rank}(B A)=\text{rank}(A)-\dim (\ker B\cap \text{range} A)\)