  In this article we provide with combinatorial proofs of some recent
identities due to Sury and McLaughlin. We show that, the solution of a general
linear recurrence with constant coefficients can be interpreted as a
determinant of a matrix. Also, we derive a determinantal expression of
Fibonacci and Lucas numbers. We prove Binets formula for Fibonacci and Lucas
numbers in a purely combinatorial way and in course of doing so, we find a
determinantal identity, which we think to be new.
