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

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] is such that A^T=A^(-1) , find alpha

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] is such that A^T=A^(-1) , find alpha .

If A=[[cosalpha, -sin alpha] , [sin alpha, cos alpha]] then A+A'=I then alpha=

If A=[ [0,-tan((alpha)/2)],[tan(alpha/2),0]] then (I-A)[[cosalpha,-sinalpha],[sinalpha,cosalpha]] =

If A_alpha=[[cosalpha ,sinalpha],[-sinalpha,cosalpha]] , then prove that A_alphaA_beta=A_(alpha+beta) for every positive integer n .

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that sinalpha+cosalpha=sqrt(2)costheta .

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that sinalpha+cosalpha=sqrt(2)costheta .

If A=[cosalpha+sinalpha,sqrt(2)sinalpha; -sqrt(2)sinalpha,cosalpha-sinalpha] , prove that A^n=[cosn\ alpha+sinn\ alpha, sqrt(2)sinn\ alpha; -sqrt(2)sinn\ alpha, cosn\ alpha-sinn\ alpha] for all n in Ndot

If A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] is identity matrix, then write the value of alpha .

If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n prove that [F(alpha)]^(-1)=F(-alpha)dot