Question

In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square

Answer 1

Step 1: Find the sum along the respective rows.

The sum of first row$=\left(1\right)+\left(-10\right)+\left(0\right)$

$$\begin{gathered} =1-10 \\ =-9 \end{gathered}$$

The sum of second row$=\left(-4\right)+\left(-3\right)+\left(-2\right)$

$$\begin{gathered} =-4-3-2 \\ =-9 \end{gathered}$$

The sum of third row$=\left(-6\right)+\left(4\right)+\left(-7\right)$

$$\begin{gathered} =-6+4-7 \\ =-9 \end{gathered}$$

Step 2: Find the sum along the respective columns.

The sum of first column$=\left(1\right)+\left(-4\right)+\left(-6\right)$

$$\begin{gathered} =1-4-6 \\ =-9 \end{gathered}$$

The sum of second column$=\left(-10\right)+\left(-3\right)+\left(4\right)$

$$\begin{gathered} =-10-3+4 \\ =-9 \end{gathered}$$

The sum of third column$=\left(0\right)+\left(-2\right)+\left(-7\right)$

$$\begin{gathered} =-2-7 \\ =-9 \end{gathered}$$

Step 3: Find the sum along the respective diagonals.

The sum of first diagonal$=\left(1\right)+\left(-3\right)+\left(-7\right)$

$$\begin{gathered} =1-3-7 \\ =-9 \end{gathered}$$

The sum of second diagonal$=\left(0\right)+\left(-3\right)+\left(-6\right)$

$$\begin{gathered} =-3-6 \\ =-9 \end{gathered}$$

As the sum of the numbers in each row, in each column and along the diagonals is same $\left(\mathrm{i}.\mathrm{e}.,-9\right)$.

Hence, the given pattern is a magic square.