We have:

$A^{\prime}=\left[\begin{array}{ccc}-1 & 5 & -2 \\ 2 & 7 & 1 \\ 3 & 9 & 1\end{array}\right], B^{\prime}=\left[\begin{array}{ccc}-4 & 1 & 1 \\ 1 & 2 & 3 \\ -5 & 0 & 1\end{array}\right]$

$A+B=\left[\begin{array}{ccc}-1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1\end{array}\right]+\left[\begin{array}{ccc}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{array}\right]=\left[\begin{array}{ccc}-5 & 3 & -2 \\ 6 & 9 & 9 \\ -1 & 4 & 2\end{array}\right]$

$\therefore(A+B)^{\prime}=\left[\begin{array}{ccc}-5 & 6 & -1 \\ 3 & 9 & 4 \\ -2 & 9 & 2\end{array}\right]$

$A^{\prime}+B^{\prime}=\left[\begin{array}{ccc}-1 & 5 & -2 \\ 2 & 7 & 1 \\ 3 & 9 & 1\end{array}\right]+\left[\begin{array}{ccc}-4 & 1 & 1 \\ 1 & 2 & 3 \\ -5 & 0 & 1\end{array}\right]$

$=\left[\begin{array}{ccc}
-5 & 6 & -1 \\
3 & 9 & 4 \\
-2 & 9 & 2
\end{array}\right]$

Hence, we have verified that $(A+B)^{\prime}=A^{\prime}+B^{\prime}$