For each of the linear functions in Exercise 7.1.51, write down its matrix representative, the matrix representative of its inverse, and verify that the matrices are mutual inverses.
Exercise 7.1.51
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

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