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

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

let alpha=pi/5 and A=[[cosalpha , sinalpha] , [-sinalpha , cosalpha]] and B=A+A^2+A^3+A^4 then: (A) B is singular (B) B is symmetric (C) B is skew symmetric (D) 0 lt |B| lt 1

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

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_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] , then

A = [ [ cosalpha , sinalpha ], [ sinalpha , cosalpha ] ] ,then find | A |

A = [ [ 1 , 0 , 0 ] , [ 0 , cosalpha , sinalpha ] , [ 0 , sinalpha , - cosalpha ] ] , find |A|

Inverse of the matrix {:[(cosalpha,-sinalpha,0),(sinalpha,cosalpha ,0),(0,0,1)]:} is