Word Count : 423

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We are given a set $$ R = \left\{ \begin{bmatrix} a & b \\ 0 & c \end{bmatrix} \,\middle|\, a, b, c \in \mathbb{R} \right\} $$ and asked to check whether $R \subseteq M_2(\mathbb{R})$ is a subring. --- ### Step 1: Recall the definition of a subring Let $M_2(\mathbb{R})$ be the ring of all $2 \times 2$ real matrices. A nonempty subset $R \subseteq M_2(\mathbb{R})$ is a subring if: 1. ______ _________ _________ _______ __________ __________ _______ ______ __________.
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