  A matrix is given in ``shredded'' form if we are presented with the multiset
of rows and the multiset of columns, but not told which row is which or which
column is which. The matrix is reconstructible if it is uniquely determined by
this information. Let $M$ be a random binary $n\times n$ matrix, where each
entry independently is $1$ with probability $p=p(n)\le\frac12$. Atamanchuk,
Devroye and Vicenzo introduced the problem and showed that $M$ is
reconstructible with high probability for $p\ge (2+\varepsilon)\frac{1}{n}\log
n$. Here we find that the sharp threshold for reconstructibility is at
$p\sim\frac{1}{2n}\log n$.
