Find (1) `|[cos theta,-sin theta],[sin theta,cos theta]|`

Evaluate the following: |costheta, -sin theta],[sin theta, cos theta]|

If E(theta)=[[cos theta, sin theta] , [-sin theta, cos theta]] then E(alpha) E(beta)=

Prove the orthogonal matrices of order two are of the form [(cos theta,-sin theta),(sin theta,cos theta)] or [(cos theta,sin theta),(sin theta,-cos theta)]

Find the distance between the points : (cos theta, sin theta), (sin theta, cos theta)

If A=[[cos theta, sin theta],[sin theta, cos theta]],B=[[cos phi, sin phi],[sin phi, cos phi]] show that AB=BA.

If A=[[cos 2 theta, sin 2 theta],[-sin2theta, cos2theta]] , find A^2

If cos2theta=0 , then |(0,costheta,sin theta),(cos theta, sin theta, 0),(sin theta, 0, cos theta)|^(2) is equal to…………

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

If the coordinates of a variable point be (cos theta + sin theta, sin theta - cos theta) , where theta is the parameter, then the locus of P is

If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos theta sin theta , sin^(2) theta , cos theta ],[sin theta ,-cos theta , 0]] ,then f ( pi / 7) is