  In this paper, firstly, we define the Qq-generating matrix for bi-periodic
Fibonacci polynomial. And we give nth power, determinant and some properties of
the bi-periodic Fibonacci polynomial by considering this matrix representation.
Also, we introduce the Hadamard products for bi-periodic Fibonacci Qnq
generating matrix and bi-periodic Lucas Qnl generating matrix of which entries
is bi-periodic Fibonacci and Lucas numbers. Then, we investigate some
properties of these products.
