Question 1094961
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<pre>
The number of 2x2 matrices comprised of numbers +/-1 in each entry/position is {{{2^4}}} = 16.


Of them, exactly 8 matrices


{{{(matrix(2,2, 1,1, 1,1))}}},  {{{(matrix(2,2, 1,-1, 1,-1))}}},  {{{(matrix(2,2, -1,1, -1,1))}}},  {{{(matrix(2,2, -1,-1, -1,-1))}}},   {{{(matrix(2,2, 1,1, -1,-1))}}},  {{{(matrix(2,2, -1,-1, 1,1))}}},  {{{(matrix(2,2, 1,-1, -1,1))}}}  and   {{{(matrix(2,2, -1,1, 1,-1))}}}


with identical or proportional rows have the determinant equal to zero.



So, the probability under the question is {{{8/16}}} = {{{1/2}}}.
</pre>

Solved.