Probability that a random binary matrix is invertible?

What is the probability that a random $\{0,1\}$, $n \times n$ matrix is invertible?
Assume the 0 and 1 are each present in an entry with probability $\frac{1}{2}$.
Is there an explicit formula as a function of $n$? Does it tend to 1 as $n$ grows large?
I’m sure this is all known…

Thanks!

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