Ring of Square Matrices over Real Numbers/Examples

Examples of Ring of Square Matrices over Real Numbers

$2 \times 2$ Real Matrices

Let $\struct {\map {\MM_\R} 2, +, \times}$ denote the ring of square matrices of order $2$ over the real numbers $\R$.

Then $\struct {\map {\MM_\R} 2, +, \times}$ forms a ring with unity which is specifically not commutative and also not an integral domain.