Question

prove that if A and B are square matrices of order n then Tr(AB)=Tr(BA).

Answer 1

This is pretty much by definition:

(AB)_ij = Sum A_ik B_kj so then write down expressions for Tr(AB) and Tr(BA) which you can see are the same....

Answer 2

please explain

Answer 3

The above is an explanation...

Write down an expression of Tr(AB) and Tr(BA) (you can do this straight from the definitions)