(a) Show that every invertible linear function L: Rn Rn can be represented by the identity matrix...

Question:

(a) Show that every invertible linear function L: Rn †’ Rn can be represented by the identity matrix by choosing appropriate (and not necessarily the same) bases on the domain and target spaces.
(b) Which linear transformations are represented by the identity matrix when the domain and target space are required to have the same basis?
(c) Find bases for which the following linear transformations on R2 are represented by the identity matrix:
(i) The scaling map 5[x] = 2x;
(ii) Counterclockwise rotation by 45°;
(iii) The shear