Paz's length conjecture for full matrix algebras

Let $\mathbb{F}$ be an arbitrary field, and let $\ell(\mathrm{M}_n(\mathbb{F}))$ denote the length of the full matrix algebra $\mathrm{M}_n(\mathbb{F})$. Paz's length conjecture.

$$\ell\big(\mathrm{M}_n(\mathbb{F})\big)=2n-2.$$

This conjecture concerns the problem of determining the length of a full matrix algebra, a linear upper-bound question originating in work of Spencer and Rivlin and formally posed by Paz. It has been proved for matrices of size at most $7$, while the general case remains open.