A is a Square matrix, and we have the following function t(A)=Σ(i=1 to n)a(ii) it equals to the sum of the diagonal elements of the matrix.
- Prove that for every matrix A,B from the same order,
t(AB)=t(BA) - Prove that there isn't any matrix A,B from order NxN so that
AB-BA = In
I was trying to prove the first and got stuck in the beginning. that was my attemp:
t(AB) = Σ(i=1 to n) Σ(j=1 to n) aij * bji
and I didn't know how to continue from here, or even if that was the right starting point.
Good start. Do the same for $t(BA)$, and then interchange the names $i$ and $j$.