Is every matrix $A \in \mathrm{SL}\_n(\mathbb C)$ a product of four unipotent matrices?


I have verified that this is true if $n = 2$, and I believe I have came across this result before. However, I cannot find a reference to this.



Is every $A \in \mathrm{SL}_n(\mathbb C)$ a product of four unipotent matrices?
In response to Qiaochu's question in the comments, Fong and Sourour prove in their paper [The group generated by unipotent operators](https://www.ams.org/journals/proc/1986-097-03/S0002-9939-1986-0840628-0/) that every element of $\mathrm{SL}\_n(\mathbb C)$ is a product of three unipotent matrices.


Edit: Sourour proves in the paper [A factorization theorem for matrices](https://dspace.library.uvic.ca/handle/1828/1594) that a nonscalar matrix in $\mathrm{SL}\_n(\mathbb C)$ is indeed a product of two unipotent matrices, confirming YCor's generalization.


