" I) If "A=[[cos alpha,cos alpha],[-sin alpha,cos alpha]]" Show that "

If A=[[cos alpha,sin alpha],[-sin alpha,cos alpha]] then show that A A^(T)=A^(T)A=I

If A,=[[cos alpha,sin alpha-sin alpha,cos alpha]] then show that ,A^(2)=[[cos2 alpha,sin2 alpha-sin2 alpha,cos2 alpha]]

A=[[Cos alpha,sin alpha],[-Sin alpha,cos alpha]] then A^(2)

A=[[cos alpha,sin alpha],[-sin alpha,cos alpha]] , then find | A |

If A= [[cos alpha, -sin alpha],[sin alpha, cos alpha]] , then A + A'= I, the value of a is :

If A(alpha)=[[cos alpha,sin alpha],[-sin alpha,cos alpha]] then A(alpha)A(beta)

If A_(alpha)=[[cos alpha, sin alpha],[ -sin alpha , cos alpha]] , then prove that i) A_(alpha ). A_(beta)=A_(alpha + beta) ii) (A_alpha)^n=[[cos n alpha, sin n alpha],[ -sin n alpha, cos n alpha]] for every positive integer n .

If A=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] then "AA"^(T)=

If A = [(cos alpha, sin alpha),(-sin alpha, cos alpha)] , then show that AA'= A'A.