Answer 1

`costheta[(costheta, sintheta),(-sintheta, costheta)] + sintheta[(sintheta, -costheta),(costheta, sintheta)]`

= `[(cos^2theta, costheta sintheta),(-costheta sintheta, cos^2theta)] + [(sin^2theta, -costheta sintheta),(costhetasintheta, sin^2theta)]`

= `[(cos^2theta + sin^2theta ,-costhetasintheta - costhetasintheta),(-costhetasintheta + costhetasintheta, cos^2theta + sin^2theta)]`

= `[(1, 0),(0, 1)]`