Statement 1: If `f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n` `[F(alpha)]^(-1)=F(-alpha)dot` Statement 2: For matrix `G(beta)=[[cosbeta,0,sinbeta],[0, 1, 0],[-sinbeta,0,cosbeta]]dot` we have `[G(beta)]^(-1)=G(-beta)dot`

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

If A=[[cosalpha, -sinalpha, 0], [sinalpha, cosalpha, 0], [0, 0, 1]] , then (adjA)^(-1)=

If F(alpha)=[[cosalpha, -sinalpha, 0], [sinalpha, cosalpha, 0], [0, 0, 1]] , where alphainR , then (F(alpha))^(-1)=

Inverse of the matrix {:[(cosalpha,-sinalpha,0),(sinalpha,cosalpha ,0),(0,0,1)]:} is

Show : [ [ cosalpha , -sinalpha ] , [ sinalpha , cosalpha ] ]= [ [1 , 0 ] , [ 0 , 1 ]]

If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))] , then A(alpha, beta)^(-1) is equal to

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

Let F(alpha)=[{:(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1):}] and G(beta)=[{:(cosbeta,0,sinbeta),(0,1,0),(-sinbeta,0,cosbeta):}] . Show that [F(alpha).G(beta)]^(-1)=G(-beta).F(-alpha) .

If F(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] and G(beta)=[(cosbeta, 0, sinbeta),(0, 1, 0),(-sinbeta, 0, cosbeta)], then [F(alpha)G(beta)]^-1 is equal to (A) F(-alpha)G(-beta) (B) G(-beta)F(-alpha0 (C) F(alpha^-1)G(beta^-1) (D) G(beta^-1)F(alpha^-1)