(i) `|(cos theta,-sin theta),(sin theta,cos theta)|`

" (1) "|[cos theta,-sin theta],[sin theta,cos 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)]

A = [(cos theta,-sin theta),(-sin theta,-cos theta)] then find A^(-1) .

The multiplicative inverse of A = [(cos theta,-sin theta),(sin theta,cos theta)]is

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

Find the characteristic roots of the two-rowed orthogonal matrix [(cos theta,-sin theta),(sin theta,cos theta)] and verify that they are of unit modulus.

Let A=[(1,0.1),(0.1,1)] S=[(cos theta ,-sin theta), (sin theta, cos theta)] Show that there exists a value of that such that S^(-1)AS is a diagonal matrix Also compute A^(100)