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Show that the most general orthogonal ma...

Show that the most general orthogonal matrix or order two is of the form
` [{:( cos theta , sin theta ),( +-sin theta , +-cos theta ):}]`

Text Solution

Verified by Experts

The correct Answer is:
`|A|^(n-2) A `
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(i) |(cos theta,-sin theta),(sin theta,cos theta)|

Inverse of the matrix [{:(cos 2 theta, -sin 2 theta),(sin 2 theta, cos 2 theta):}] is

(1 + sin theta-cos theta) / (1 + sin theta + cos theta)

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

cos theta/(1+sin theta)=(1-sin theta)/cos theta

Inverse of the matrix [(cos 2 theta,-sin 2theta),(sin 2 theta, cos 2theta)] is

(1 + sin theta-cos theta) / (1 + sin theta + cos theta) =

((sin theta+cos theta)^(2)-1)/(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)]