If `A_alpha=[(cos alpha, sin alpha),(-sin alpha, cos alpha)].` Prove that

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

If A(alpha)=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] then the matrix A^(2)(alpha) is

A_(alpha )= [(cos alpha, sin alpha),(- sin alpha, cos alpha)] 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)^(n) = A(n alpha) " where " n in N

If A_(alpha)=[cos alpha sin alpha-sin alpha cos alpha], then prove that (A_(alpha))^(n)=[cositive in n alpha-s in n alpha cos n alpha] for every positive integer n.

If A(alpha)=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] , then A(alpha)A(beta)=

If A_(alpha), = [{:(cos alpha , sin alpha),(-sin alpha , cos alpha):}] , then

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 .