There are two relationship discusses in this tesis, that is the relationship of Lucas matrix Ln and p-Tribonacci matrix T p n , and the relationship of Fibonacci matrix Fn and p-Tribonacci matrix T p n . These relationship are to obtain a new matrix called Ep n matrix and Hp n matrix, then the Ep n matrix and Hp n can be expressed in the form Ln = T p n Ep n and Fn = T p n Hp n. …