The left ideal of matrix ring

Question

I want to know the left ideals of a matrix ring. For example, given a matrix ring $R = M_2(\mathbb{Z}/N\mathbb{Z})$. When $N$ is a prime, the left ideals of $R$ is $\begin{pmatrix}a & b \\0 & 0\end{pmatrix} $, where $(a,b) \in \mathbb{P}^1(\mathbb{Z}/N\mathbb{Z})$ the number of left ideals are $N+1$. My question is when $N$ is not a prime, left ideals of $R$ are the same as above?