Question

I need a solution for this problem with extra details

10. If B is a square matrix and A is the exponential of B, defined by the infinite series expansion of the exnonential, As e 1+B+B2+. . +-+..., ?" n! 2 then prove the following properties (a) eLeC-eB+C, prov?ding B and C commute (b) A-1-e-B (c) e (d) A is orthogonal if B is antisymmetnc. CBC1 CAC

The book is Goldstein classical mechanics 3rd edition and the chapter   4.10

Answer 1

Cive thal 2 2. 2. 2

匂 2 2 2 피 CAC BA Tne e 3 -0 ence Ce (e

3 ul und X-