induction

ITT some proof by induction.

>>6
{{cos(x), -sin(x)}, {sin(x), cos(x)}} = e^({{0, -x}, {x, 0}}).

Substituting nx for x in the latter gives e^({{0,-nx}, {nx, 0}}). This is, of course, equal to {{cos(nx), -sin(nx)}, {sin(nx), cos(nx)}}.