[" 16."pi/9quad A_(alpha)=[[cos alpha,sin alpha],[-sin alpha,cos alpha]]],[" (i) "A_(alpha)*A_(beta)=A alpha+beta]

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

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

If A_(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] , 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

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

If A_(alpha)=[(cos alpha,sinalpha),(-sinalpha,cosalpha)] then A_(alpha) A_(beta) is equal to A) A_(alpha beta) B) A_(alpha +beta) C) A_(alpha - beta) D)None of these

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