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 = [(cos alpha sin alpha),(-sinalpha, cosalpha)] , prove (by inducton ) that A^n = [(cos n alpha, sinnalpha),(-sin n alpha cosn alpha)] for all positive integral n.

If A=[(cos alpha,sinalpha),(-sinalpha,cosalpha)] , prove by induction that A^n=[(cosnalpha,sinnalpha),(-sinnalpha,cosnalpha)],n in N

If A=[(cos alpha,sinalpha),(-sinalpha,cosalpha)] , verify that A'A=I_2

If A={:((cosalpha,sinalpha),(-sinalpha,cosalpha)):} , prove by mathematical induction that , A^(n)={:((cosnalpha,sinnalpha),(-sinnalpha,cosnalpha)):} where n(ge2) is a positive integer.

If A=[(cosalpha,sinalpha),(-sinalpha,cosalpha)] prove that A.A^(T)=1 Hence find A^(-1)

If A= [[cosalpha,sinalpha],[-sinalpha,cosalpha]] then show that A^2=[[cos2alpha,sin2alpha],[-sin2alpha,cos2alpha]]

If A = [(cos alpha , sin alpha),(-sinalpha, cosalpha)] , verify that AA' = I_2 = A'A

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] ,show that A^2=[[cos2alpha,sin2alpha],[-sin2alpha,cos2alpha]]

If A = [(cosalpha, sinalpha),(-sinalpha,cosalpha)] prove that, A A^(') = I. Hence, find A^(-1) .

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