Chapter 7.3, Problem 29P

To determine

(a)

To proof:

The matrix $A$ is always similar to itself.

To determine

(b)

To proof:

If $A$ is similar to $B$, then $B$ is similar to $A$.

To determine

(c)

To proof:

If $A$ is similar to $B$ and $B$ is similar to $C$, then $A$ is similar to $C$.