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

Flind the product of two matrices A =[[cos^(2) theta , cos theta sin theta],[cos theta sin theta ,sin^(2)theta]] B= [[cos^(2) phi,cos phi sin phi],[cos phisin phi,sin^(2)phi]] Show that, AB is the zero matrix if theta and phi differ by an odd multipl of pi/2 .

If A = [[cos^2theta, costhetasintheta],[costhetasintheta, sin^2theta]] B= [[cos^2phi, cosphisinphi], [cosphisinphi, sin^2phi]] and theta - phi = (2n+1)(pi)/2 Find AB.

sin^(3)theta + sin theta - sin theta cos^(2)theta =

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)]

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

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0

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

(4) A=[[cos(theta),sin(theta)],[-sin(theta),cos(theta)]] ; prove, A^n=[[cos(ntheta),sin(ntheta)],[sin(ntheta),cos(ntheta)]]

Prove that: sin4 theta=4 sin theta cos^(3)theta-4cos theta sin^(3)theta