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

If F(alpha)=[[cos alpha,-sin alpha, 0],[sin alpha, cos alpha, 0],[0,0,1]] , then show that F(alpha) F (beta)= F(alpha + beta) .

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

Let F(alpha)=[[cos alpha,-sin alpha,0sin alpha,cos alpha,00,0,1]], where alpha in R Then (F(alpha))^(-1) is equal to F(alpha^(-1)) b.F(-alpha) c.F(2 alpha)d.-[[1,11,0]]

Find inverse of the matrix A=[[cos alpha, -sin alpha, 0 ],[ sin alpha, cos alpha, 0],[ 0, 0, 1]]

If F(alpha)=|(cos alpha, -sin alpha, 0),(sin alpha, cos alpha, 0),(0,0,1)| then det F(alpha)=

If F(alpha)=[[cos alpha,0,sin alpha],[0,1,0],[-sin alpha,0,cos alpha]] , show that [F(alpha]^(-1)=F(-alpha) .

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 .