Let $A=(a_{ij})$ with $1\leq i,j\leq n\in\mathbb{N}$ be a square matrix with complex coefficients. Then the following inequality holds: $$|\det(A)|\leq \prod_{i=1}^n\left(\sum_{j=1}^n|a_{ij}|^2\right)^\frac{1}{2}.$$ Moreover, if $A$ is Hermitian and positive semidefinite, the following inequality holds: $$\det(A)\leq \prod_{i=1}^n a_{ii},$$ with equality if and only if $A$ is a diagonal matrix.