Solution space of a system and its rank

Solution space of a system and its rank

If I know that A is an m by n matrix, B is an n by m matrix, rank(A) =
rank(B) = rank(AB) = m and that AB = I_m: how can I show that the solution
space of Ax=0 is the same as for (BA)x = 0 and how can I find rank(BA).
Any hints or help will be appreciated.