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To find number of 4 cross 4 matrices, such that each element is 1 or -1. Also sum of elements in each row and each column should be zero.

I am able to think that each row and each column shall consist of two 1 and two -1. But then how to proceed further

answer is 90

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Hint: across any row and down any column, your choice in the first three elements uniquely determines the fourth. As such, you can consider the number of $3 \times 3$ matrices with entries in $\{1,-1\}$ such that no row/column $\mathbf v$ has $v_1 = v_2 = v_3$ i.e. all entries are the same.

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  • $\begingroup$ so how does it solve. $\endgroup$
    – maveric
    Mar 18 '19 at 18:53
  • $\begingroup$ please give solution $\endgroup$
    – maveric
    Mar 19 '19 at 2:12
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Arrange two columns. 6*6 which is 36. Now for each such arrangement other two columns gets fixed in two ways. So 72

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  • $\begingroup$ Answer is 90.somebody please help. $\endgroup$ Mar 20 '19 at 14:03
  • $\begingroup$ @Brian could you please check the answer $\endgroup$ Mar 20 '19 at 14:04

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