Abstract In this paper, we studied and found the new matrices of 3×3, which it have similar properties to Fibonacci Q −matrix. Moreover, we studied and found the matrix formula 1 1 2 2 0 2 0 1 0 0 2 1 1 0 0 1 1 1 1 3 0 1 1 1 3 n n n n n n n n F L Q F L F L + + + +           =     =                   when n F and n L are Fibonacci and Lucas sequences, respectively.