If `A_alpha=[cosalphasinalpha-sinalphacosalpha]` , then prove that `A_alphaA_beta=A_(alpha+beta)` for every positive integer `n` .

If A_alpha=[[cosalpha ,sinalpha],[-sinalpha,cosalpha]] , then prove that A_alphaA_beta=A_(alpha+beta) for every positive integer n .

If A_(alpha)=[cos alpha sin alpha-sin alpha cos alpha], then prove that A_(alpha)A_(beta)=A_(alpha+beta) for every positive integer n.

If A_(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] , then prove that A_(alpha)A_(beta)=A_(alpha+beta) .

A_(alpha )= [(cos alpha, sin alpha),(- sin alpha, cos alpha)] then prove that A_(alpha . A_(beta) = A_(alpha + beta)

If A_(alpha)=[[cos alpha, sin alpha],[ -sin alpha , cos alpha]] , then prove that i) A_(alpha ). A_(beta)=A_(alpha + beta) ii) (A_alpha)^n=[[cos n alpha, sin n alpha],[ -sin n alpha, cos n alpha]] for every positive integer n .

If A_alpha = [(cos alpha, sin alpha),(-sin alpha, cos alpha)] , then what is the value of A_alphaA_beta .

Consider the matrix A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] Show that A_(alpha)A_(beta)=A_(alpha+beta)

If A_alpha=[cosalphasinalpha-sinalphacosalpha],t h e nA_alphaA_beta= (a)A_(alpha+beta) (b) A_(alphabeta) (c) A_(alpha-beta) (D) None of these

If A_alpha=[cosalphasinalpha-sinalphacosalpha] , then prove that (A_alpha)^n=[cos n\ alphasinn\ alpha-sinn\ alpha cos n\ alpha] for every positive integer n .