let $X=\{X_0, X_1,\ldots \}$ be a finite or countable set, $K$ a field, and $K\langle X\rangle$ the free associative algebra generated by $X$.
It is known that all associative algebras, generated by a finite or countable number of elements, can be represented as the factor ring $K\langle X\rangle/I$, where $I$ is an ideal of $K\langle X\rangle$.
If we considere the matrix algebra $M_n(K)$, over the field $K$, what is the representation of this algebra in the form $K\langle X\rangle/I$?