Show the following, using matrices, combinations of linear transformations, and trigonometric identities. You must prove these in general – an example is not sufficient.
(i) The combination of a rotation and a reflection is a reflection,
(ii) Any rotation can be written as a combination of two reflections.
My Input : Considering (a,b) as a general point of reference. So (-b, a) 90 degree rotation ;(-a, -b) 180 degree rotation; (b, -a) 270 degree rotation (a, -b) reflection over x-axis; (-a, b) reflection over y-axis; (b, a) reflection over y=x; (-b, -a) reflection over y= -x
Now First let us say 90 degree rotation and then reflection over x-axis So (a,b) -> (-b,a) -> (b,-a) . This we can say as 270 degree rotation so this is not a reflection. I am confused . Please help me with detailed explanation on this . Thank you !