pls solve correctly. skip if you are not sure of your solution. thank you!.

Problem 2: Two-level systems and exponential operators (6 points) (a) (4 points) Show that (a . a) (b . 6) = a . b1 +i(a x b) . o where o is a vector that has the Pauli matrices as its components and a, b are ordinary three-component vectors. Hint: You can use the Pauli matrix commutators and anti-commutators. (b) (2 points) Use the above result to show that: e izm.d = COS N/6 1 - i(m . o) sin 10/6 where m is an arbitrary unit vector (|m| = 1)