Question

Show that the eigenvalues of a null matrix are zero.​

Answer 1

Step-by-step explanation:

If v is a non-zero eigen vector corresponding to an eigenvalues λ we have, by definition, Av=λv.

Then A2v=A(Av)=A(λv)=λ2v. It easily follows that λn is an eigenvalue for An but the latter is the zero matrix, for which all eigenvalues are zero, hence λ=0.