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

**Solution:**

A magic square is an array of numbers where the sum of rows, columns, and diagonal elements are equal.

Let us consider the square (i)

**On adding the numbers in each row 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 column 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 of the 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 row 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 column 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 of the 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.}

**☛ Check: **Class 7 Maths NCERT Solutions Chapter 1

**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

**Summary:**

In a magic square each row, column and diagonal have the same sum. The second square box is the magic square since each row, column, and diagonal have the same sum whereas the first square box is not a square box as it sum of diagonal elements are not equal.

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