Please show the steps clearly and explain.

Define S : 2 - R2 by ac - 2y S 1) = 3x - y and define T : R2 - R3 by x + y = x - y 2x + 3yWith S and T from the previous problem, a) Find a matrix, A such that TX = AX. b) Find a matrix, B such that SX = BX. c) Find a matrix, C, for the transformation TS. d) Verify AB = C. e) Find and range(TS). f) Find, if possible " urs ( ) - g) Find, if possible ar s ( ) - 1:]