# Matrix inverse's existential crisis

Consider the matrix

$A = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}$

with $$P(a_{ij} = 0) = P(a_{ij} = 1) = \frac{1}{2}$$ for all entries.

If the probability that $$A$$ is invertible can be expressed as $$\frac{m}{n}$$, where $$m$$ and $$n$$ are positive coprime integers, find $$m+n$$.

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