i was trying to figure out something that i didn't understand and the book doesn't have much examples of it either. My question is how do u know whether a transformation is a projection on a line, reflection on a line, or rotation through an angel? With T given. The questions i did from the book, i was able to find the line and reflection, since the same question was previously stated and i was able to do it, n got the answer from there, but didn't understand it. Take T[x y]=1/2[x-y y-x] and by solving these i get [1 -1]/[-1 1] (this is not division, just goes at the bottom, its a 2x2 matrix, and the vectors r transposed) so by looking at this [ 1 -1] [-1 1] how can u tell whether its a reflection, projection or rotation? Similarly another result i got for another part was [1/2 root3/2] [root3/2 1/2 ] i think this one is rotation but how can u tell?