grandes-ecoles 2019 Q3

grandes-ecoles · France · centrale-maths1__pc Matrices Matrix Algebra and Product Properties

Suppose $n \geqslant 3$. Are the subsets $\mathrm{S}_{n}(\mathbb{K})$ and $\mathrm{A}_{n}(\mathbb{K})$ subalgebras of $\mathcal{M}_{n}(\mathbb{K})$?

Suppose $n \geqslant 3$. Are the subsets $\mathrm{S}_{n}(\mathbb{K})$ and $\mathrm{A}_{n}(\mathbb{K})$ subalgebras of $\mathcal{M}_{n}(\mathbb{K})$?