Detection of knots and a cabling formula for A-polynomials

We say that a given knot J ⊂ S is detected by its knot Floer homology and A-polynomial if whenever a knot K ⊂ S has the same knot Floer homology and the same A-polynomial as J , then K = J . In this paper we show that every torus knot T (p, q) is detected by its knot Floer homology and A-polynomial. We also give a one-parameter family of infinitely many hyperbolic knots in S each of which is detected by its knot Floer homology and A-polynomial. In addition we give a cabling formula for the A-polynomials of cabled knots in S, which is of independent interest. In particular we give explicitly the A-polynomials of iterated torus knots.