Evaluate the following: ` |[cosalpha, sinalpha],[sinalpha, cosalpha]| `

Select and write the correct answer from the given alternatives in each of the following:If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] ,then A A' =

If A=[[cosalpha, sinalpha], [-sinalpha, cosalpha]] , then A^(10)=

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

If A=[(cas alpha, sinalpha),(-sinalpha,cosalpha)], AA'=

Select the correct option from the given alternatives.If A = [[cosalpha,sinalpha],[-sinalpha,cosalpha]] then A^-1 = ? 1) [[frac{1}{cosalpha},-frac{1}{sinalpha],[frac{1}{sinalpha},frac{1}{cosalpha]] 2) [[cosalpha,-sinalpha],[sinalpha,cosalpha]] 3) [[-cosalpha,sinalpha],[-sinalpha,cosalpha]] 4) [[-cosalpha,sinalpha],[sinalpha,-cosalpha]]

Show that the matrix: A = {:[(cosalpha, -sinalpha),(sinalpha,cosalpha)] is orthogonal.

If A=[ [0,-tan((alpha)/2)],[tan(alpha/2),0]] then (I-A)[[cosalpha,-sinalpha],[sinalpha,cosalpha]] =

If A = {:[(cosalpha, sinalpha),(-sinalpha, cosalpha)] , then find A^2

Show : [ [ cosalpha , -sinalpha ] , [ sinalpha , cosalpha ] ]= [ [1 , 0 ] , [ 0 , 1 ]]

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