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Q.3 In a “magic square” the sum of number in each row, in each column and along the diagonals is the same. Is this a magic square?

Answer :

Along first row = \(\frac{4}{11}+\frac{9}{11}+\frac{2}{11} =\frac{15}{11} \)
Along second row = \(\frac{3}{11}+\frac{5}{11}+\frac{7}{11}=\frac{15}{11} \)
Along third row = \(\frac{8}{11}+\frac{1}{11}+\frac{6}{11}=\frac{15}{11} \)
Along first column= \(\frac{4}{11}+\frac{3}{11}+\frac{8}{11}=\frac{15}{11} \)
Along second column= \(\frac{9}{11}+\frac{5}{11}+\frac{1}{11}=\frac{15}{11} \)
Along third column= \(\frac{2}{11}+\frac{7}{11}+\frac{6}{11}=\frac{15}{11} \)
Along first diagonal= \(\frac{4}{11}+\frac{5}{11}+\frac{6}{11}=\frac{15}{11} \)
Along second diagonal= \(\frac{2}{11}+\frac{5}{11}+\frac{8}{11}=\frac{15}{11} \)
Since, the sum of all the fraction row wise, column wise and the diagonal wise is same i.e. \(\frac{15}{11} \). Hence, it is a magic square.