2 questions i need help with:

1.Show that if a 6x6 matrix A has a negative determinant, then A has at least one positive eigenvalue (Hint: sketch the graph of the characteristic polynomial)

2. Consider an eigenvalue lambda of an nxn matrix A. we know that lambda is an eignvalue of Atranspose as well (since A and Atranspose have the same characteristic polynomial). Compare the geometric multiplicities of lambda as an eignvalue of A and A transpose