a) Show that the matrices

A =

2 3 5

7 11 13

17 19 23

and

B =

29 31 37

41 43 47

53 59 61

are not similar.

b)

Show that the matrices A =

7 2

24 7

and B =

0 1

1 0

are similar: find an invertible

matrix S such that B = S^1AS. (Hint: first show that A and B are both similar to the

same diagonal matrix D, then find S.)