Chapter 8.PS, Problem 20PS

To determine

(a)

To find:

The $2\times 2$ matrix and a $3\times 3$ matrix in the form of $A$

To determine

(b)

To find:

The higher powers of matrices $B$ and $C$ with the use graphing utility and Describe the result.

To determine

(c)

To find:

A conjecture about powers of $A$ when $A$ is a $4\times 4$ matrix.

To determine

(d)

To find:

The conjecture about powers of $A$ with the use of result of part (b) and (c) when $A$ is an $n\times n$ matrix.