Homework Statement
Show that A = 3 4 3
-1 0 -1
1 2 3
is not diagonalizable but is triangulable and carry out triangulation (A has rational entries)
I found that the only eigenvalue is 2, and that the characteristic equation is (x-2)3, but I'm...
Homework Statement
Show that if A is nilpotent then det(I-A)=det(I+A)=1.
Homework Equations
I know that det(A)=0 if A is nilpotent and det(I)=1, so this seems like it follows logically. I also know that the tr(A)=0 and that tr(I-A)=tr(I+A)=n, and that the characteristic polynomial of...