Determine which of the following linear functions L: R2 R2 has an inverse, and, if so, describe

Question:

Determine which of the following linear functions L: R2 †’ R2 has an inverse, and, if so, describe it:
(a) The scaling transformation that doubles the length of each vector;
(b) Clockwise rotation by 45°;
(c) Reflection through the y axis;
(d) Orthogonal projection onto the line y = .v;
(e) The shearing transformation defined by the matrix