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

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]]

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

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

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=[(cos alpha,sin alpha),(-sin alpha,cos alpha)] and A. adj A=[(k,0),(0,k)] , then k is equal to

If p & q are lengths of perpendicular from the origin x sin alpha + y cos alpha = a sin alphacos alpha and x cos alpha-y sin alpha = acos 2alpha, then 4p^2 + q^2

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

If (2sin alpha)/({1+cos alpha + sin alpha})=y, then ({1-cos alpha+sin alpha})/(1+sin alpha)=