Being A and B n*n matrices, such that AB=BA+A, show that A is not invertible. And the proof shall be done by contradiction and using the properties of the trace of matrices to prove it. I got tr(AB)=tr(BA+A)
tr(AB)=tr(BA)+tr(A)
tr(AB)=tr(AB)+tr(A)
tr(A)=0
what can I conclude from this that will help me though?