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)

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

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, 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 = [(cos alpha,sin alpha),(-sin alpha,cos alpha)] , then A^(10) = .........

A_((alpha))=[{:(cos alpha,-sin alpha),(sin alpha,cos alpha):}],A_((beta))=[{:(cos beta,-sin beta),(sin beta,cos beta):}] Which one of the following is correct ?

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