Solve `abs[[costheta,-sintheta],[sintheta,costheta]]`

Evaluate the determinates abs([-costheta,-sin theta],[sintheta,-costheta])

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

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

Evaluate- |[costheta,sintheta],[sintheta,costheta]|

If A=[[costheta, sintheta], [-sintheta, costheta]] , then

If A=[[costheta, sintheta], [-sintheta, costheta]] , then |A^(-1)|=

If A=[[costheta,sintheta],[-sintheta,costheta]] and beta=A^4+A then determinant of beta=

Show that every real orthogonal matrix is of any one of the forms {:[(costheta,-sintheta),(sintheta,costheta)]:}or{:[(costheta,sintheta),(sintheta,-costheta)]:}

costheta[{:(costheta,-sin theta),(sintheta,costheta):}]+sintheta[{:(sintheta,costheta),(-costheta,sintheta):}]=?

Let A={:[(costheta,-sintheta),(-sintheta,-costheta)]:} then inverse of A is