`if A=[{:(costheta,sin theta ),(-sin theta,costheta):}]`, then show that : `A^(2)=[{:(cos2theta,sin2theta),(-sin2theta,cos2theta):}]`

Let A = [ (cos theta, sin theta),(- sin theta, cos theta)] , then show that A ^(2) = [(cos 2 theta, sin 2 theta),( - sin 2 theta, cos 2 theta)]

If A=[[costheta,sintheta],[-sintheta,costheta]] then prove that A^2=[[cos2theta,sin2theta],[-sin2theta,cos2theta]]

(sintheta+sin2theta)/(1+costheta+cos2theta)

(sintheta+sin2theta)/(1+costheta+cos2theta)

(sintheta+sin 2theta)/(1+costheta+cos2theta)=

(sintheta+sin2theta)/(1+costheta+cos2theta) =

(sintheta+sin2theta)/(1+costheta+cos2theta)=?

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?

The inverse of the matrix [(cos2theta, -sin2theta),(sin2theta, cos2theta)] is -

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?