Well done, but black retaking with the king left his rook en prise, he should have taken with the rook instead.  Similarly, white's preceding move was kind of a waste as it saves the black rook.  Yuo should have taken out the black rook first.

Alls well that ends well though.  You started out with a won position and you ended with a won position, even if black had chosen to save his rook.  Nice going!