Question 151
Let $A \in \mathcal{M}_n(\mathbb{R})$ be a matrix with the property that
$$
\det(A + X) \ge \det X, \text{ for all } X \in \mathcal{M}_n(\mathbb{R}).
$$
Prove that $A = O_n$.
$$
\det(A + X) \ge \det X, \text{ for all } X \in \mathcal{M}_n(\mathbb{R}).
$$
Prove that $A = O_n$.