જો $A=\left[\begin{array}{rrr}-1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1\end{array}\right]$ અને $B=\left[\begin{array}{rrr}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{array}\right],$ હોય,તો ચકાસો કે $(A-B)^{\prime}=A^{\prime}-B^{\prime}$.

(A) સૌ પ્રથમ,$A-B$ ની ગણતરી કરો:
$A-B = \left[\begin{array}{rrr}-1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1\end{array}\right] - \left[\begin{array}{rrr}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{array}\right] = \left[\begin{array}{rrr}3 & 1 & 8 \\ 4 & 5 & 9 \\ -3 & -2 & 0\end{array}\right]$
હવે,પરિવર્તિત શ્રેણિક $(A-B)^{\prime}$ શોધો:
$(A-B)^{\prime} = \left[\begin{array}{rrr}3 & 4 & -3 \\ 1 & 5 & -2 \\ 8 & 9 & 0\end{array}\right]$
આગળ,$A^{\prime}$ અને $B^{\prime}$ શોધો:
$A^{\prime} = \left[\begin{array}{rrr}-1 & 5 & -2 \\ 2 & 7 & 1 \\ 3 & 9 & 1\end{array}\right]$,$B^{\prime} = \left[\begin{array}{rrr}-4 & 1 & 1 \\ 1 & 2 & 3 \\ -5 & 0 & 1\end{array}\right]$
હવે,$A^{\prime}-B^{\prime}$ ની ગણતરી કરો:
$A^{\prime}-B^{\prime} = \left[\begin{array}{rrr}-1 & 5 & -2 \\ 2 & 7 & 1 \\ 3 & 9 & 1\end{array}\right] - \left[\begin{array}{rrr}-4 & 1 & 1 \\ 1 & 2 & 3 \\ -5 & 0 & 1\end{array}\right] = \left[\begin{array}{rrr}3 & 4 & -3 \\ 1 & 5 & -2 \\ 8 & 9 & 0\end{array}\right]$
આમ,$(A-B)^{\prime} = A^{\prime}-B^{\prime}$ હોવાથી,ગુણધર્મ ચકાસાયેલ છે.