Let `A=[(cos theta, -sin theta),(- sin theta,-cos theta)]` then the inverse of a is

Options

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

Answer

A

Explanation

`|A| = |{:(cos theta , - sin theta), (- sin theta , - cos theta):}|= -1`
and (A) = `[{:(- cos theta , sin theta ) , (sin theta , cos theta):}]`
`therefore A^(-1) = |{:(cos theta , - sin theta ) , (- sin theta , - cos theta):}| = A`