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

Taking rows 

5 + (–1) + (–4) = 5 – 5 = 0

(–5) + (-2) + 7 = –7 + 7 = 0

 0 + 3 + (–3) = 3 – 3 = 0 

Taking columns 

5 + (–5) + 0 = 5 – 5 = 0 

(–1) + (–2) + 3 = –3 + 3 = 0

 (–4) + 7 + (–3) = 7 – 7 = 0 

Taking diagonals 

5 + (–2) + (–3) = 5 – 5 = 0

(–4) + (–2) + 0 = –6 

This box is not a magic square because all the sums are not equal.

(ii) 

Taking rows 

1 + (–10) + 0 = 1 – 10 = –9

 (–4) + (–3) + (–2) = –7 – 2 = –9

 (–6) + 4 + (–7) = –2 – 7 = –9

 Taking columns

 1 + (–4) + (–6) = 1 – 10 = –9

 (–10) + (–3) + 4 = –13 + 4 = –9 

0 + (–2) + (–7) = 0 – 9 = –9

 Taking diagonals

 1 + (–3) + (–7) = 1 – 10 = –9

 0 + (–3) + (–6) = –9

 This box is magic square because all the sums are equal.

(i) From the (i) square
1^st row 5 + (-1) + (-4) = 0
2^nd row -5 + -2 + 7 = 0
3^rd row 0 + 3 + -3 = 0
1^st column 5 + -5 + 0 = 0
2^nd column -1 + -2 + 3 = 0
3^rd column -4 + 7 – 3 = 0
1^st Diagonal 5 + -2 + -3 = 0
2^nd Diagonal 0 + -2 + -4 = -6
∴ It is not a magic square.

(ii) 1^st row 1 + -10 + 0 = -9
2^nd row – 4 + -3 – 2 = -9
3^rd row -6 + 4 – 7 = -9
1^st column 1 + – 4 – 6 = -9
2^nd column -10 + -3 + 4 = -9
3^rd column 0 + – 2 – 7 = -9
1^st Diagonal – 6 – 3 + 0 = -9
2^nd Diagonal 1 – 3 – 7 = -9
∴ It is a magic square.

In the first square,
If we check the sum of each row and each column in the first square, it comes `0`.
However, if we check the sum of numbers on diagonals, it comes `0` and `-6`.
As one of the diagonal have different sum than the sum of rows and columns, this is not a magic square.

In the second square,
If we check the sum of each row and each column in the second square, it comes `-9`.
If we check the sum of numbers on diagonals, it comes `-9` and `-9`.
As the sum of each row, column and diagonal have the same sum, this is a magic square.