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.

Explanation

We have,
`|A-lambdaI|=|(cos theta - lambda,-sin theta),(sin theta,cos theta - lambda)|`
`=(cos theta-lambda)^(2)+sin^(2) theta`
Therefore, characteristic equation of A is
`(cos theta-lambda)^(2)+sin^(2) theta=0`
or `cos theta-lambda= pm i sin theta`
or `lambda=cos theta pm i sin theta`
Which are of unit modulus.