If `A=[(cos theta, sin theta),(-sin theta, cos theta)]`, then prove that `A^n=[[cosntheta,sin ntheta],[-sin ntheta,cos ntheta]], n in N`

If A=[[cos theta, sin theta],[ -sin theta, cos theta]] , then prove that A^n=[[cos ntheta, sinn theta],[ -sin n theta, cos n theta]] , n in N .

If A=[(costheta,sintheta),(-sintheta,costheta)] , then prove that A^(n)=[(cosntheta,sin n theta),(-sin ntheta,cos n theta)], n in N .

If A=[[cos theta,sin theta-sin theta,cos theta]] then prove that A^(n)=[[cos n theta,sin n theta-sin n theta,cos n theta]],n in N

Answer the following questions.If A=[[costheta,sintheta],[-sintheta,costheta]] ,prove that A^n=[[cos ntheta,sin ntheta],[-sin ntheta,cos ntheta]] , for all n in N

Show that if A = [[cos theta, sin theta],[-sin theta, cos theta]] , then A^n = [[cos n theta, sin n theta],[-sin n theta, cos n theta]]

(4) A=[[cos(theta),sin(theta)],[-sin(theta),cos(theta)]] ; prove, A^n=[[cos(ntheta),sin(ntheta)],[sin(ntheta),cos(ntheta)]]

If A = ([cos theta,sin theta],[-sin theta,cos theta]) show that A= ([cos ntheta,sin n theta],[-sin n theta,cos n theta]) n= positive integer.

If A=[(cos theta, sin theta),(- sin theta, cos theta)] then lim_(nto oo)1/n A^(n) is

cosm theta - sin ntheta =0