Let A and B be the 2 2 real matrices A = a b b a , B = 0

Let A and B be the 2 × 2 real matrices A =

 a −b b a 

, B =

 λ 0 1 λ



.

Show that eA = ea

 cos b − sin b sin b cos b



, eB = eλ

 1 0 1 1 

.

(Hints: Note that 2 × 2 matrices of the form
a −b b a are isomorphic to the complex numbers under the correspondence
a −b b a

↔ a + bi.

For the second case write B = λI + C.)