Supppose a is an invertible n\times n matrix and v is an eigenvector of a with associated eigenvalue -3. convince yourself that v is an eigenvalue of the following matrices, and find the associated eigenvalues:
1. \ a^6, \ eigenvalue = ,
2. \ a^{-1}, \ eigenvalue = ,
3. \ a + 5 i_n, \ eigenvalue = ,
4. \ 6 a, \ eigenvalue = .