If `A=[[cosalpha, sinalpha],[-sinalpha, cosalpha]]`, prove by mathematicasl induction that, `A^n=[[cosnalpha, sin nalpha],[-sin nalpha,cos nalpha]]` for every natural number n

If A=[[cosalpha, -sin alpha] , [sin alpha, cos alpha]] then A+A'=I then alpha=

If A=[[cosalpha, sin alpha] , [-sin alpha, cos alpha]] and A^(-1)=A' then alpha=

If A_(alpha)=[cos alpha sin alpha-sin alpha cos alpha], then prove that (A_(alpha))^(n)=[cositive in n alpha-s in n alpha cos n alpha] for every positive integer n.

If A=[(sinalpha,cosalpha),(-cosalpha,sinalpha)] , the prove that A'A=I .

If A=[cos theta i sin theta i sin theta cos theta], then prove by principle of mathematical induction that A^(n)=[cos n theta i sin n theta i sin n theta cos n theta] for all n in N.

If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] , show that A^(2)=[{:(cos2alpha,sin2alpha),(-sin2alpha,cos2alpha) :}].

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 cosalpha+cosbeta=0=sinalpha+sinbeta , then cos2alpha+cos2beta=?

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