Number of matrices , such that sum in each row and each column is 0

Question

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

Answer 1

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.

Answer 2

Arrange two columns. 6*6 which is 36. Now for each such arrangement other two columns gets fixed in two ways. So 72