Finding the right ideals of $M_{n\times n}(\mathbb{F})$ (matrices over a field $\mathbb{F}$)

Question

I'm trying to figure out all the possible right ideals of $M_{n\times n}(\mathbb{F})$.

I know that the two-sided ideals are only the trivial ones, and the proof uses the fact that we can operate on the rows and line of a matrix to make $E_{ij}$ - the matrix that has one in ij and zero in the rest of it.

Does anyone have any idea(l)?

Thanks.