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)`.

A_(alpha )= [(cos alpha, sin alpha),(- sin alpha, cos alpha)] then prove that A_(alpha . A_(beta) = A_(alpha + beta)

If A = [[cos alpha,sin alpha],[-sin alpha,cos alpha]] , then verify that A'A = I

A_(alpha )= [(cos alpha, sin alpha),(- sin alpha, cos alpha)] then prove that (A_(alpha)^(n) = A(n alpha) " where " n in N

If A= [[cos alpha, -sin alpha],[sin alpha, cos alpha]] , then A + A'= I, the value of a is :

Find A^2 if A = [(cos alpha, sinalpha),(-sin alpha, cos alpha)]

Write the value of |[[cos alpha,-sin alpha],[sin alpha,cos alpha]] from the following :

If F(theta) = [(cos theta, - sin theta, 0),(sintheta, costheta, 0),(0,0,1)] and G(alpha) = [(cos alpha, 0, sin alpha),(0,1,0),(-sinalpha, 0, cos alpha)] , show that [F(theta) G(alpha)]^-1 = G ( - alpha ) F ( - theta)

If tan theta=(sin alpha- cos alpha)/(sin alpha+cos alpha) , then:

If A=[{:(cos alpha, -sin alpha),(sin alpha,cos alpha):}] then A+A'=I, if the value of alpha is ……