Evaluate
`[[costheta,sintheta],[-sintheta,costheta]]`

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

Simplify costheta[[costheta,sintheta],[sintheta,costheta]]+sintheta[[sintheta,-costheta],[costheta,sintheta]]

Find the inverse of the following matrix: |[costheta,sintheta],[-sintheta,costheta]|

If A=[[costheta,sintheta],[-sintheta,costheta]],then Lim_(x_>oo)1/nA^n is

Statement 1: If A is an orthogonal matrix of order 2, then |A|=+-1. Statement 2: Every two-rowed real orthogonal matrix is of any one of the forms [[costheta ,-sintheta ],[sintheta ,costheta]]or[[costheta ,sintheta],[ sintheta,-costheta]]dot

If A=[[costheta,sintheta],[-sintheta,costheta]] , then for any natural number, find the value of D e t\ (A^n) .

If A=[[costheta,-sintheta],[sintheta,costheta]] then show that A^n = [[cosntheta,-sinntheta],[sinntheta,cosntheta]]

If A=[[costheta -sintheta], [[sintheta , costheta]]] , then find the values of theta satisfying the equation A^T+A=I_2 .

Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta.[{:(sintheta,-costheta),(costheta,sintheta):}]=I.

Find the inverse of the matrix [(costheta ,sintheta) ,( -sintheta ,costheta )] .