  We consider a strongly correlated ladder with diagonal hopping and exchange
interactions described by $t-J$ type hamiltonian. We study the dynamics of a
single hole in this model in the presence of a static non-magnetic (or
magnetic) impurity. In the case of a non-magnetic (NM) impurity we solve the
problem analytically both in the triplet (S=1) and singlet (S=0) sectors. In
the triplet sector the hole doesn't form any bound state with the impurity.
However, in the singlet sector the hole forms bound states of different
symmetries with increasing $J/t$ values. Binding energies of those
impurity-hole bound states are compared with the binding energy of a pair of
holes in absence of any impurity. In the case of magnetic impurity the
analytical eigenvalue equations are solved for a large (50 X 2) lattice. In
this case also, with increasing $J/t$ values, impurity-hole bound states of
different symmetries are obtained. Binding of the hole with the impurity is
favoured for the case of a ferromagnetic (FM) impurity than in the case of
antiferromagnetic (AFM) impurity. However binding energy is found to be maximum
for the NM impurity. Comparison of binding energies and various impurity-hole
correlation functions indicates a pair breaking mechanism by NM impurity.
