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

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :

If A(alpha,beta)=[[cosalpha,sinalpha,0],[-sinalpha,cosalpha,0],[ 0, 0,e^(beta)]],t h e nA(alpha,beta)^(-1) is equal to a. A(-alpha,-beta) b. A(-alpha,beta) c. A(alpha,-beta) d. A(alpha,beta)

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

If A=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]] , find a d j\ A and verify that A(a d j\ A)=(a d j\ A)A=|A|I_3 .

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

If A=[(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),( 0, 0, 1)], find a d jdotA and verify that A(a d jdotA)=(a d jdotA)A=|A|I_3dot

If A=[{:(sinalpha,-cosalpha,0),(cosalpha,sinalpha,0),(0,0,1):}] then A^(-1) is equal to

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