" If "A_(alpha)=([cos alpha,sin alpha],[-sin alpha,cos alpha])," then "(A_(alpha))^(3)=?

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

A=[[Cos alpha,sin alpha],[-Sin alpha,cos alpha]] then A^(2)

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 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]]. Prove that

A=[[cos alpha,sin alpha],[-sin alpha,cos alpha]] , then find | A |

Let A_(alpha)=[[cos alpha,-sin alpha,osin alpha,cos alpha,00,0,1]]

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 prove that A_(alpha)A_(beta)=A_(alpha+beta) for every positive integer n.