If `F(x)= [[cosx, -sinx,0],[sinx, cosx, 0],[0,0,1]]`,then which of the following are correct?

If F(x)=[[cosx,-sinx,0],[sinx,cosx,0],[0,0,1]] Show that F(x)F(y)=F(x+y)

If f(x) = [(cos x , - sinx,0),(sinx,cosx,0),(0,0,1)] then show f(x) . f(y) = f(x+y)

If A=[{:(cosx,sinx,0),(-sinx,cosx,0),(0,0,1):}] =f(x), then A^(-1) is equal to

If A=f(x)=[(cosx, sinx, 0),(-sinx, cosx,0),(0,0,1)], then the value of A^-1= (A) f(x) (B) -f(x) (C) f(-x) (D) -f(-x)

If F(x)=[{:(cosx,-sinx,0),(six,cosx,0),(0,0,1):}] , show that F(x).F(y)=F(x+y).

f(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] Statement 1: f(x) is inverse of f(-x) Statement 2: f(x).f(y) = f(x+y)

If |[cosx, sinx, cosx], [-sinx, cosx, sinx], [-cosx, -sinx, cosx]|=0 , then x=

F(x)=[[cosx,-sinx,0],[sinx,cosx,0],[0,0,1]] and G(x)=[[cosx,0,sinx],[0,1,0],[-sinx,0,cosx]], then [F(x)G(y)]^(-1) is equal to (A) F(-x)G(-y) (B) F(x-1)G(y-1) (C) G(-y)F(-x) (D) G(y^(-1))F(x^(-1))

If A=[(cosx,sinx),(-sinx,cosx)] and A.(adjA)=k[(1,0),(0,1)] then the value of k is