" 2."(i)|[cos theta,-sin theta],[sin theta,cos theta]|

Evaluate the following determinants: (b) |(cos theta, -sin theta),(sin theta, cos theta)| = cos theta (cos theta) - sin theta(-sin theta) = cos^(2) theta + sin^(2) theta = 1

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

Verify that [(cos theta, sin theta),(-sin theta, cos theta)] and [(cos theta, - sin theta),(sin theta, cos theta)] are inverse of each other.

Simplify: cos theta[[cos theta , sin theta],[-sin theta , cos theta]]+sin theta[[sin theta, -cos theta],[cos theta ,sin theta]] .

Simplify cos theta[(cos theta,sin theta),(-sin theta,cos theta)]+sin theta[(sin theta,-cos theta),(cos theta,sin theta)]

Simplify : cos theta[(cos theta,sin theta),(-sin theta,cos theta)]=sin theta[(sin theta,-cos theta),(cos theta,sin theta)]

If A = [(cos theta, sin theta),(-sin theta, cos theta)] and B = [(sin theta, - cos theta), (cos theta, sin theta)] , evaluate A cos theta + B sin theta .

Let A = [ (cos theta, sin theta),(- sin theta, cos theta)] , then show that A ^(2) = [(cos 2 theta, sin 2 theta),( - sin 2 theta, cos 2 theta)]

If cos theta{:((cos theta, sin theta),(-sin theta, cos theta)):}+ sin theta{:((x,-cos theta),(cos theta, x)):}=I_(2) , find x.