The Padovan numbers have the Q-matrix, Q =⎡0 1 00 0 11 1 0⎤⎦. The Q-matrix is a 3 × 3 matrix that when raised to the n^th power give a matrix whose entries are Padovan numbers. For which we established by mathematical induction that, Qn =⎡⎣Pn−1 Pn+1 PnPn Pn+2 Pn+1Pn+1 Pn+3 Pn+2⎤⎦ , for all n ≥ 3.