How to slove this question?

#7 * Consider a matrix A with the special property that 11'\" = A for some positive integer 111 Such a matrix is special, and as such we might expect it to have special eigenvalues, Say 1r is an eigenvector of A with eigenvalue t, By leftmultiplying in times by the matrix A we get Amv 2 Av Since v is an eigenvector with eigenvalue 1% this translates into tmv : hr. Since the only way this can be satised is it :7\" : t, implying that the eigenvalues of A must be , An example of such a matrix is 2 5 3 B : 1 3 2 1 0 1 Here m = 5 and the eigenvalues are the set :] l