If `E(theta)=|[costheta,sintheta],[-sintheta,costheta]|`, then `|E^3(theta)|=`

If {:A=[(cos theta,sintheta),(-sintheta,costheta)]:}," then A.A' is

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

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

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

If A=[[costheta,sintheta],[-sintheta,costheta]] then prove that A^2=[[cos2theta,sin2theta],[-sin2theta,cos2theta]]

Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]

Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]

Simplify costheta[(costheta,sin theta),(-sintheta,costheta)]+sintheta[(sintheta,-costheta),(costheta,sintheta)]

costheta[[costheta, sintheta], [-sintheta, costheta]]+sintheta[[sintheta, -costheta], [costheta, sintheta]]=

Simplify costheta[(costheta,sin theta),(-sintheta,costheta)]+sin[(sintheta,-costheta),(costheta,sintheta)]