Answer the following questions. If`A_alpha=[[cosalpha,sinalpha],[-sinalpha,cosalpha]]`,show that `A_alpha.A_beta=A_(alpha+beta)`

Answer the following questions.If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[0,0,1]] then f(-alpha)

Answer the following questions. If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[0,0,1]] f(-alpha)+f(alpha)

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] ,show that A^2=[[cos2alpha,sin2alpha],[-sin2alpha,cos2alpha]]

Answer the following questions.If A=[[cosalpha,-sinalpha],[sinalpha,cosalpha]] and A+A^T=I ,where I is unit matrix 2x2,then find the value of alpha

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] ,show that A^TA=I ,where I is the unit matrix of order 2.

Select the correct option from the given alternatives. If F(alpha) = [[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[0,0,1]] where alpha in R then [F(alpha)]^-1 is

Select and write the correct answer from the given alternatives in each of the following:If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] ,then A A' =

Select the correct option from the given alternatives.If A = [[cosalpha,sinalpha],[-sinalpha,cosalpha]] then A^-1 = ? 1) [[frac{1}{cosalpha},-frac{1}{sinalpha],[frac{1}{sinalpha},frac{1}{cosalpha]] 2) [[cosalpha,-sinalpha],[sinalpha,cosalpha]] 3) [[-cosalpha,sinalpha],[-sinalpha,cosalpha]] 4) [[-cosalpha,sinalpha],[sinalpha,-cosalpha]]

If tan beta=(n sin alpha cos alpha)/(1-n sin^2alpha) , show that tan(alpha-beta)=(1-n)tan alpha dot