Singularity of random Bernoulli matrices

Understand

For each $n$, let $M_n$ be an $n\times n$ random matrix with independent $\pm 1$ entries.

• We show that ${\mathbb P}\{\mbox{$M_n$ is singular}\}=(1/2+o_n(1))^n$, which settles an old problem.
• Some generalizations are considered.