7. Let V = Mat (2 2, R) be the vector space of all 2 2 matrices with real coefficients and let T: VV be the map T(X) AX-XA where A = (} }). (a) Show that T is a linear map. (b) Find the matrix representation [7]s of T with respect to the basis B={ (69) ( ) ( ) (89) (c) Consider that basis B' = { 5-(( ) ( ) ( ) ( ) for V. Find the transition matrix P = [id]B.B (d) Use the results above to express the matrix representation [T]g of T with respect to B (e) Find bases for the kernel and the image of T.