A 2D geometric shape is rotated about a point with coordinates (1,2)  by 90°  in a clockwise direction.  Then, the shape is scaled about the same point in the x-coordinate by 2 times and in the y-coordinate by 3 times. Finally, the shape is reflected about the origin.  Derive the single combined transformation matrix for these operations.

Answer: The sequence of transformations is as follows. 

From right to left the sequence is as follows- (i) Translate so that (1,2) moves to origin (ii) Rotate about the origin by -90°  (iii) Scale by (2,3) (iv) Translate back so that (1,2)  is at its previous position (v) Flip about the origin. Single combined transformation can be obtained by multiplying all these matrices.