An eigenvalue of a matrix, A, is a value such that for some non-zero vector v. That is the same as . Since v= 0 is an obvious solution to that problem, we are saying that this must not have a unique solution and so must not have an inverse. A condition that it not have an inverse is that its determinant is 0. So we have the "characteristic equation" which, for this matrix, is

Expanding on the first row, that is

i) What are the real roots of that? Can you find the eigenvector?

ii) What are the complex roots of that? can you find the eigenvectors?