Suppose that A is a 33 matrix with eigenvalues 1 1 2 2 and 3

Suppose that A is a 3×3 matrix with eigenvalues 1 =1, 2 =2, and 3 =3.
(a) Find the eigenvalues of A¹.
(b)Find the eigenvalues of B = A² 2A + I. (I is the 3 × 3 identity matrix).

(c) Find the eigenvalues of B² A².

(d) Find the eigenvalues of C = (A I)(A 2I)(A 3I).
(e)Is it true that C is the zero matrix? Verify your answer.

Solution