જો $A=\begin{bmatrix}-1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1\end{bmatrix}$ અને $B=\begin{bmatrix}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{bmatrix}$ હોય,તો ચકાસો કે $(A+B)^{\prime}=A^{\prime}+B^{\prime}$.

(A) આપણી પાસે છે:
$A^{\prime}=\begin{bmatrix}-1 & 5 & -2 \\ 2 & 7 & 1 \\ 3 & 9 & 1\end{bmatrix}, B^{\prime}=\begin{bmatrix}-4 & 1 & 1 \\ 1 & 2 & 3 \\ -5 & 0 & 1\end{bmatrix}$
$A+B=\begin{bmatrix}-1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1\end{bmatrix}+\begin{bmatrix}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{bmatrix}=\begin{bmatrix}-5 & 3 & -2 \\ 6 & 9 & 9 \\ -1 & 4 & 2\end{bmatrix}$
$\therefore (A+B)^{\prime}=\begin{bmatrix}-5 & 6 & -1 \\ 3 & 9 & 4 \\ -2 & 9 & 2\end{bmatrix}$
$A^{\prime}+B^{\prime}=\begin{bmatrix}-1 & 5 & -2 \\ 2 & 7 & 1 \\ 3 & 9 & 1\end{bmatrix}+\begin{bmatrix}-4 & 1 & 1 \\ 1 & 2 & 3 \\ -5 & 0 & 1\end{bmatrix}=\begin{bmatrix}-5 & 6 & -1 \\ 3 & 9 & 4 \\ -2 & 9 & 2\end{bmatrix}$
આમ,$(A+B)^{\prime} = A^{\prime}+B^{\prime}$ સાબિત થાય છે.