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

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 what is the value of A_alphaA_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 f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then

If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))] , then A(alpha, beta)^(-1) is equal to

If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))] , then A(alpha, beta)^(-1) is equal to

If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))] , then A(alpha, beta)^(-1) is equal to