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I can't figure out how to find all left ideals of the ring $$M_2(\mathbb R)= \left\{\begin{bmatrix}a&b\\c&d\end{bmatrix}\quad |\quad a,b,c,d \in \mathbb{R} \right\}.$$

Thanks in advance.

user26857
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Alper
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  • Hint: what can you say about the rows of the matrix multiplication $AB$, where $B$ is in the ideal and $A$ is arbitrary? – Gal Porat Mar 14 '17 at 18:59

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