Doing some last minute homework, and stuck on this one. Although its due in 4 hours thought its worth a shot.

Our assignment is to "Use a property of determinants to show that A and A^T have the same characteristic polynomial."

I know that (A - LI)x = 0, where L = lambda.

Not sure how to prove that with something like

det(A-LI) = 0? No idea.

Also, one other: Show that if A and B are similar, then det A = det B