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

**Solution:**

Let us consider the square (i)

**On adding the numbers in each rows we get,**

1st Row = 5 + (- 1) + (- 4) = 5 - 1 - 4 = 5 - 5 = 0

2nd Row = -5 + (-2) + 7 = - 5 - 2 + 7 = -7 + 7 = 0

3rd Row = 0 + 3 + (-3) = 3 - 3 = 0

**On adding the numbers in each columns we get,**

1st Column = 5 + (- 5) + 0 = 5 - 5 = 0

2nd Column = (-1) + (-2) + 3 = -1 - 2 + 3 = -3 + 3 = 0

3rd Column = -4 + 7 + (-3) = -4 + 7 - 3 = -7 + 7 = 0

**On adding the numbers in diagonals we get,**

1st Diagonal = 5 + (-2) + (-3) = 5 - 2 - 3 = 5 - 5 = 0

2nd Diagonal = -4 + (-2) + 0 = - 4 - 2 = -6

Since, sum of one diagonal is not equal to zero,

**So, (i) is not a magic square**

Now, let us consider the square (ii)

**On adding the numbers in each rows we get,**

1st Row = 1 + (-10) + 0 = 1 - 10 + 0 = -9

2nd Row = (-4) + (-3) + (-2) = -4 - 3 - 2 = -9

3rd Row = (-6) + 4 + (-7) = -6 + 4 - 7 = -13 + 4 = -9

**On adding the numbers in each columns we get,**

1st Column = 1 + (-4) + (-6) = 1 - 4 - 6 = 1 - 10 = -9

2nd Column = (-10) + (-3) + 4 = -10 - 3 + 4 = -13 + 4 = -9

3rd Column = 0 + (-2) + (-7) = 0 - 2 - 7 = -9

**On adding the numbers in diagonals we get,**

1st Diagonal = 1 + (-3) + (-7) = 1 – 3 – 7 = 1 – 10 = -9

2nd Diagonal = 0 + (-3) + (-6) = 0 – 3 – 6 = -9

_{This square box is a magic square because each row, column, and diagonal have the same sum.}

_{Hence, (ii) is a magic square.}

**Video Solution:**

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

### NCERT Solutions Class 7 Maths - Chapter 1 Exercise 1.1 Question 7

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

The second square box is the magic square since each row, column, and diagonal have the same sum