# Tag Archives: binary vectors

## Random matrices and pentagonal numbers

Here is a clever problem:

Let us fix $n$. Take at random, with uniform probability, a $n \times n$ binary matrix (call it $A$).
Let: $\gamma_n = P[\det_{Z_2}(A)=1]$.
(You can think of it as taking determinant of matrix normally and asking for a probability that it is odd number.)
Find the value of: $\gamma = \lim_{n\to\infty} \gamma_n$

(It’s not that gamma! Although, it is still related to Euler!)