Consider matrices of the form

(a) Write a 2 × 2 matrix and a 3 × 3 matrix in the form of A.
(b) Use a graphing utility to raise each of the matrices to higher powers. Describe the result.
(c) Use the result of part (b) to make a conjecture about powers of A when A is a 4 × 4 matrix. Use the graphing utility to test your conjecture.
(d) Use the results of parts (b) and (c) to make a conjecture about powers of A when A is an n × n matrix.

ain a14 a13 0 412 a23 A : u( - 1)