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

(i) 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.

7 Maths Chapter 1 Exercise 1.1 Question 7, 8

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