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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.

(i) 

5-1-4
-5-27
03-3

(ii) 

1-100
-4-3-2
-64-7

1 Answer

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Best answer

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.

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