There is a linear transformation T from R2 to R2 that reflects a vector about the x-axis, then rotate it clockwise by π/3 about the origin and then reflects a vector about the line y = -x.
Determine if the transformation T is invertible or not. If it is invertible, find the standard matrix of the inverse of T.
How could I determine the invertibility of the linear transformation? I calculated the standard matrix of T, and it is 2*2, is it enough to prove T is invertible? Are finding the standard matrix of the inverse of T the same as finding the inverse of the standard matrix of T? I am a little bit confused about the invertibility of a linear transformation. Could someone explain the meaning behind that?