given that A is an nxn matrix, how do you show that the characteristic polynomial of A is (-1)^n det(A)?
Doing magic because the above is far from being true. In fact, $\displaystyle (-1)^n\det A$ is not even a polynomial of degree n, let alone
the characateristic polynomial of any nxn matrix. Read carefully again the question and repost.
Tonio
PS Perhaps there is something about some free coefficient or stuff...?