In image editing software such as Photoshop generally express positions with respect to an (x, y) coordinate system with some origin (0, 0). Rotation about (0, 0) can be thought of as a linear operation on the coordinates. In a 300 × 400 image with bottom-left corner at the origin, the bottom right corner is rotated to (288, 84) and the top left corner is rotated to (−112, 384).

(a) Write down the matrix R describing this rotation.

(b) What would applying R−1 do to an image?