We introduce a uniformly distributed random variable $C : \Omega \rightarrow \mathcal{M}_{n}(\{-1,1\})$. For $\omega \in \Omega$, we denote by $C_{i,j}(\omega)$ the coefficients of the matrix $C(\omega)$.
Show that for all $t \geqslant 0$, we have
$$\mathbb{P}\left(M(C) \geqslant t n^{3/2}\right) \leqslant \exp\left(-\left(\frac{t^{2}}{2} - 2\ln 2\right)n\right).$$