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

Options

A. `[{:(-cos theta, sin theta),(-sin theta, -cos theta):}]`
B. `[{:(cos theta, sin theta),(-sin theta, cos theta):}]`
C. `[{:(-cos theta, -sin theta),(sin theta, -cos theta):}]`
D. `[{:(cos theta, sin theta),(sin theta, -cos theta):}]`

Answer

B

Explanation

`|A|=cos ^(2)+sin^(2)theta=1`
`adj(A)=[{:(cos theta,sintheta),(-sin theta, cos theta):}]`
`A^(-1)=(adj(A))/(|A|)=[{:(cos theta, sin theta),(-sin theta, cos theta):}]`