In a magic square each row, column and diagonals have the same sum. Check which of the following is a magic square.$( i)$.

$5$	$-1$	$-4$
$-5$	$-2$	$7$
$0$	$3$	$-3$

$( ii)$.

1	−10	0
−4	−3	−2
−6	4	−7

Solution:

Let us check both the squares to find the magic square.

In sqaure $( i)$:

Let us find the sum of each row, column and diagonal:

In first row: $5-1-4=0$

In second row: $-5-2+7=0$

In third row: $0+3-3=0$

In first column: $5-5+0=0$

In second column: $-1-2+3=0$

In third row: $-4+7-3=0$

In first diagonal: $5-2-3=0$

In second diagonal: $0-2-4=-6$

Here, sum of second diagonals values is different.

Thus, square $( i)$ is not a magic square. 

In square $( ii)$:

 In first row: $1-10+0=-9$

In second row: $-4-3-2=-9$

In third row: $-6+4-7=-9$

In first column: $1-4-6=-9$

In second column: $-10-3+4=-9$

In third column: $0-2-7=-9$

In first diagonal: $1-3-7=-9$

In second diagonal: $-6-3+0=-9$

Here, sum of values of each row, column and diagonals is the same.

Thus, square $( ii)$ is a magic square. 

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Updated on: 10-Oct-2022

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