What is $\mathcal{M}_{2}(\mathbb{R})$

Question

I came across $\mathcal{M}_{2}(\mathbb{R})$ in my exercise book on algebra, but there was no mention of it in the lesson. How is it defined or what should I reference to find a definition. It doesn't look like the usual $\,\!M_2(\mathbb{R})$

Answer 1

These two things should be the same. Some authors use $\mathcal{M}_2(\mathbb{R})$ and others use the unadorned $M_2(\mathbb{R})$, but they both mean $2\times 2$ matrices with coefficients in $\mathbb{R}$.