If `A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]]`,show that `A^TA=I`,where I is the unit matrix of order 2.

Answer the following questions.If A=[[cosalpha,-sinalpha],[sinalpha,cosalpha]] and A+A^T=I ,where I is unit matrix 2x2,then find the value of alpha

Answer the following questions. If A_alpha=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] ,show that A_alpha.A_beta=A_(alpha+beta)

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

If A=[[3,1],[-1,2]] prove that A^2-5A+7I=O ,where I is unit matrix of order 2.

Select the correct option from the given alternatives. If F(alpha) = [[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[0,0,1]] where alpha in R then [F(alpha)]^-1 is

If A=[[1,-2],[5,3]],B=[[1,-3],[4,-7]] ,then find the matrix A-2B+6I , where I is the unit matrix of order 2.

If A=[[5,4],[-2,3]] and B=[[-1,3],[4,-1]] ,then find C^T such that 3A-2B+C=I ,where I is the unit matrix of order 2.

If A=[[1,0],[-1,7]] find k so that A^2-8A-kI=O ,where I is a unit matrix and O is a null matrix of oreder 2.