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प्रश्न
If A = [aij] is a skew-symmetric matrix, then write the value of \[\sum_i \sum_j\] aij.
उत्तर
\[Given: A = \left[ a_{ij} \right] \text{is a skew symmetric matrix} . \]
\[ \Rightarrow a_{ij} = - a_{ji} \left[ \text{For all values of i}, j \right]\]
\[ \Rightarrow a_{ii} = - a_{ii} \left[ \text{For all values of i} \right]\]
\[ \Rightarrow a_{ij} = 0\]
\[Now, \]
\[ \sum^{}_i \sum^{}_j a_{ij} = a_{11} + a_{12} + a_{13} + . . . + a_{21} + a_{22} + a_{23} + . . . + a_{31} + a_{32} + a_{33 + . . .} \]
\[ = 0 + a_{12} + a_{13} + . . . - a_{12} + 0 + a_{23} + . . . - a_{13} - a_{23} + 0 + . . . \]
\[ = 0\]
\[Thus, \]
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