$$A = \begin{bmatrix}1 & 1 & 1 \\1 & 1 & 1 \\1 & 1 & 1 \end{bmatrix} \Rightarrow A^{2019} =$$

$$A = \begin{bmatrix}1 & 1 & 1 \\1 & 1 & 1 \\1 & 1 & 1 \end{bmatrix} \

by help of $$$$$$A = \begin{bmatrix}a1 & a2 & a3 \\b1 & b2 & b3\\c1 & c2 & c3 \end{bmatrix} \

$$$$$$A = \begin{bmatrix}a2*b3+b2*a3 & a1*c3+c1*a3 & a1*b2+a2*b1 \\\end{bmatrix} \

$$$$$$A = \begin{bmatrix}1*1+1*1 & 1*1+1*1 & 1*1+1*1 \\\end{bmatrix} \

$$$$$$A = \begin{bmatrix}2 & 2 & 2 \\\end{bmatrix} \

$$$$$$A = 2\begin{bmatrix}1 & 1 & 1 \\1 & 1 & 1 \\1 & 1 & 1 \end{bmatrix} \

A^{2019} = 3^{2018}\begin{bmatrix}1 & 1 & 1 \\1 & 1 & 1 \\1 & 1 & 1 \end{bmatrix} \

A^{2019} = 3^{2018}\begin{bmatrix}A \end{bmatrix} \